Scale - AutoCAD

1. What should the other spacing measure after the operation?
   Answer: It should measure $10$ units. When you use AutoCAD's SCALE command with the Reference option, you're telling the software to resize selected geometry by a ratio derived from two lengths: the current (reference) measurement and the desired target measurement. Every dimension within the selected geometry scales by that same uniform factor — that's the key insight here. The scale factor is calculated as: $\text{Scale Factor} = \frac{\text{New Length}}{\text{Reference Length}} = \frac{50}{47.6} \approx 1.0504$ Applying this to the second spacing: $9.52 \times 1.0504 \approx 10.0 \text{ units}$ So the correct answer is C — the spacing becomes exactly $10$ units, which makes sense: both measurements were proportionally "undersized" by the same ratio, and scaling corrects them simultaneously. A ($9.066$ units) represents a shrinkage, as if you divided instead of multiplied — flipping the scale factor upside down. B ($9.52$ units) reflects the misconception that only the referenced dimension changes while everything else stays fixed; in reality, SCALE transforms all selected geometry uniformly. D ($11.92$ units) comes from mistakenly doubling the scale factor or applying an additive offset rather than a multiplicative ratio — a common arithmetic trap. A helpful strategy: whenever you see SCALE with Reference on the exam, immediately compute $\frac{\text{new}}{\text{reference}}$ to find the scale factor, then multiply every other dimension by that same value. Clean ratios like $\frac{50}{47.6}$ that produce round results on secondary dimensions are a strong signal you've set up the problem correctly.
2. Which scaling result correctly converts the selected geometry to millimeters?
   Answer: Use factor $25.4$; the edge becomes $203.2$ units. When geometry moves between drawings with different unit assumptions in AutoCAD, no automatic rescaling happens — you must manually apply a scale factor to convert the physical meaning of the numbers. The key relationship to memorize is that $1 \text{ inch} = 25.4 \text{ mm}$, which drives every inch-to-millimeter conversion. Here, the original drawing treats 1 unit as 1 inch, but the destination drawing treats 1 unit as 1 mm. To preserve the real-world size, every unit value must be multiplied by $25.4$. An edge reading $8$ units (meaning 8 inches) must become $203.2$ units (meaning 203.2 mm), because $8 \times 25.4 = 203.2$. That makes C correct. Choice A applies the factor $0.03937$, which is actually $\frac{1}{25.4}$ — the conversion going the opposite direction, from millimeters to inches. Using it shrinks the geometry drastically instead of enlarging it. Choice B uses a factor of $8$, which is simply the current edge length — there is no logical reason to scale by the length of one edge; this produces a meaningless result. Choice D multiplies by $203.2$, which is itself the target length of that one edge, not a unit-conversion factor. Applying it cascades a single edge's converted value as if it were a ratio, producing a wildly oversized result. A reliable study tip: always anchor unit-conversion scaling to the ratio $\frac{\text{destination unit size}}{\text{source unit size}}$. Inches to millimeters → multiply by $25.4$. Millimeters to inches → multiply by $0.03937$. Getting the direction backwards is the most common trap on this type of question.
3. Which geometry exists when the command is completed?
   Answer: The original line from $x=20$ to $x=50$ and a copy from $x=20$ to $x=80$. When working with AutoCAD's SCALE command, the key concept to understand is the difference between a standard scale operation and one that uses the Copy option. Normally, SCALE transforms the original object in place — it's destructive. The Copy option changes this behavior entirely, preserving the original geometry while producing a scaled duplicate. Here's how the math works: your original line spans from $x=20$ to $x=50$, giving it a length of $30$ units. The base point is set at $x=20$. When you scale by a factor of $2$ from that base point, every point on the object moves to twice its distance from $x=20$. The left endpoint stays at $x=20$ (distance of $0 \times 2 = 0$), and the right endpoint moves to $x=20 + (30 \times 2) = x=80$. Because you used Copy, the original line from $x=20$ to $x=50$ is retained, and the new scaled line from $x=20$ to $x=80$ is added — making B the correct answer. Choice A describes the result of a standard SCALE without Copy — the original would be gone, replaced by the scaled version. Choice C reflects a misunderstanding of how the base point works; if the base point were at $x=0$, the endpoints would double to $x=40$ and $x=100$, but anchoring at $x=20$ keeps that endpoint fixed. Choice D would only make sense if a scale factor of $1$ were used, which would produce an identical overlapping copy. A helpful rule of thumb: whenever you see the Copy option inside a modify command (SCALE, ROTATE, MIRROR), think "original stays, transformed version is added."
4. Which result correctly describes the circles after scaling?
   Answer: Centers at $10$ and $25$; diameters of $4$ and $6$. Whenever you see a scaling question in AutoCAD, remember that the SCALE command transforms geometry relative to the base point — meaning every point in the drawing moves closer to or farther from that base point by the scale factor. This affects both the position of objects and their size. Here's how it works mathematically: when you scale by $0.5$ about $x = 0$, every x-coordinate is multiplied by $0.5$. So the circle centers move from $20$ and $50$ to $20 \times 0.5 = 10$ and $50 \times 0.5 = 25$. The diameters also scale: $8 \times 0.5 = 4$ and $12 \times 0.5 = 6$. That gives you centers at $10$ and $25$ with diameters of $4$ and $6$ — confirming answer A is correct. Answer B keeps the centers at their original positions, which would only be true if the base point were at each circle's own center — it isn't. The centers absolutely move when the base point is external. Answer C correctly recalculates the center positions but leaves the diameters unchanged, confusing a move operation with a scale operation — scaling always resizes the geometry too. Answer D uses incorrect center values ($20$ and $35$) that don't follow from any standard scaling logic, likely representing a random arithmetic error. A reliable tip: always ask yourself two questions when scaling — "Where do the centers go?" (multiply coordinates by the factor relative to the base point) and "How do the sizes change?" (multiply all dimensions by the same factor). Both change together.
5. What is the resulting x-coordinate of the other endpoint?
   Answer: The endpoint moves to $x=100$. When working with AutoCAD's SCALE command, the critical concept to understand is that scaling stretches or shrinks an object relative to its base point. The base point itself never moves — only the distances from the base point change. Here's how to think through it: the original endpoint sits at $x = 70$, and the base point is at $x = 10$. First, find the distance from the base point to the endpoint: $70 - 10 = 60$ units. Applying a scale factor of $1.5$ multiplies that distance: $60 \times 1.5 = 90$ units. Finally, add that new distance back to the base point: $10 + 90 = 100$. The endpoint moves to $x = 100$, confirming that A is correct. As for the wrong answers: B ($x = 105$) likely comes from mistakenly multiplying the entire original coordinate by $1.5$ ($70 \times 1.5 = 105$), which ignores the role of the base point entirely. C ($x = 90$) is a partial calculation — it's the scaled distance ($90$ units) without adding the base point's position back in, making it an easy arithmetic trap. D claims the endpoint doesn't move at all, which would only be true if the scale factor were $1.0$. A reliable strategy: always break SCALE problems into three steps — find the distance from base point to the object, multiply by the scale factor, then add the result back to the base point coordinate. Never scale the raw coordinate directly.
6. Which scale factor should be entered in the SCALE command?
   Answer: Enter a scale factor of $1.5625$. When using AutoCAD's SCALE command, you're applying a multiplier to the object's current size — so the core calculation is always: $\text{Scale Factor} = \dfrac{\text{New Length}}{\text{Old Length}}$. Keeping this formula in mind will cut through any confusion the question tries to create. Here, you need to go from $24$ units to $37.5$ units, so: $\dfrac{37.5}{24} = 1.5625$. Since the result is greater than $1$, the object gets larger — which makes sense, because $37.5 > 24$. Answer A is correct. As for the wrong answers: B ($0.64$) is the reciprocal trap — it's roughly $\frac{24}{37.5}$, which is what you'd use if you were shrinking from $37.5$ down to $24$, not growing in the other direction. Students who flip the numerator and denominator land here. C ($13.5$) comes from subtracting instead of dividing: $37.5 - 24 = 13.5$. The SCALE command uses multiplication, not addition, so the difference between the two lengths is completely irrelevant. D ($0.5625$) is a believable distractor because it looks like a proper decimal scale factor, but it would shrink the object to about half its size rather than enlarging it. A quick study tip: whenever a SCALE question gives you both a current and target dimension, always divide new ÷ old. If the result is above $1$, you're enlarging; below $1$, you're shrinking. That sanity check alone will help you eliminate wrong answers instantly.
7. Which result should the user expect?
   Answer: Width $36$, height about $84.71$, with the hinge point fixed. When using AutoCAD's SCALE command with the Reference option, the key concept to understand is that the scale factor applies uniformly in all directions — and the base point remains fixed while everything else stretches proportionally around it. Here's how to think through it: the Reference option calculates a scale factor by dividing the new value by the reference value. In this case, the factor is $\frac{36}{34} \approx 1.0588$. AutoCAD then applies this same factor to every dimension of the object. So the new height becomes $80 \times \frac{36}{34} \approx 84.71$ units. The selected base point — the hinge point — stays locked in place while the rest of the symbol scales outward from it. That confirms D as the correct answer: width $36$, height approximately $84.71$, with the hinge point fixed. A gets the geometry right (width $36$, height ≈ $84.71$) but incorrectly states that the center is fixed. The base point you select — not the center — is what remains stationary. B assumes only the width changes while the height stays at $80$. This would describe a non-uniform stretch (like the STRETCH command), not a proportional scale. SCALE always affects all axes equally. C invents a height of $82$, which has no mathematical basis. It may seem like a reasonable "add 2 to match the width increase," but that's arithmetic, not proportional scaling. A useful tip: on AutoCAD exam questions involving SCALE with Reference, always compute $\frac{\text{new}}{\text{old}}$ and apply it universally — and remember that your chosen base point never moves.
8. What will be the resulting length of the bracket edge?
   Answer: The edge becomes $180$ units long. When using the Reference option in AutoCAD's SCALE command, you're defining a scaling ratio — not anchoring specific points or setting an absolute length for a particular edge. The ratio is: $\text{scale factor} = \dfrac{\text{new reference length}}{\text{old reference length}}$. This factor then applies uniformly to the entire object, regardless of which two points you used to measure the reference distance. Here, the reference points are $60$ units apart, and you specify a new length of $90$ units for that same distance. That gives a scale factor of $\dfrac{90}{60} = 1.5$. AutoCAD then multiplies every dimension in the object by $1.5$, so the bracket edge becomes $120 \times 1.5 = 180$ units — confirming D is correct. Choice A ($80$ units) likely comes from subtracting: $120 - (90 - 60) = 90$… actually it may come from dividing $120 \div 1.5 = 80$, confusing which direction the scale goes — dividing instead of multiplying. Choice B ($90$ units) is the most tempting trap: students assume the Reference option directly sets the edge to the new reference length of $90$, but that's not how it works — it only defines the scale ratio. Choice C ($150$ units) might come from adding the $30$-unit increase from the reference ($90 - 60 = 30$) directly onto $120$, treating it as an absolute offset rather than a proportional scale. The key study tip: whenever you see Reference in a SCALE question, immediately compute the ratio $\dfrac{\text{new}}{\text{old}}$ and multiply it by the actual object dimension — never assume the new reference value directly becomes any edge's length.
9. Which statement correctly describes the expected result?
   Answer: A factor of $1.25$ produces $150$ by $75$, so one SCALE operation cannot meet both dimensions. Whenever you see a question about AutoCAD's SCALE command, remember one fundamental rule: SCALE applies a single uniform factor to all dimensions simultaneously. There is no way to stretch width independently of height using a standard SCALE operation — that requires STRETCH or non-uniform scaling tools. Here's the math that makes B correct. To bring the width from $120$ to $150$, you need a scale factor of $\frac{150}{120} = 1.25$. Because SCALE is uniform, that same $1.25$ multiplier applies to the height as well: $60 \times 1.25 = 75$. The result is $150 \times 75$, not $150 \times 60$. Since the height requirement of $60$ units is violated, one standard SCALE operation simply cannot satisfy both constraints at once — exactly what B states. Answer A describes the Reference option within SCALE, which lets you type an existing length and a new length instead of a direct factor. However, Reference still computes a uniform factor ($\frac{150}{120} = 1.25$) and applies it to every axis. The height would still become $75$, not $60$. A incorrectly implies Reference scales only the referenced direction. Answer C is nonsensical — a factor of $1$ changes nothing at all, so the width stays at $120$, not $150$. Answer D inverts the ratio ($\frac{120}{150} = 0.8$), which would actually shrink the width to $96$, not enlarge it to $150$. Study tip: Anytime a question asks whether SCALE can resize an object to specific dimensions in one step, check whether the width ratio and height ratio are equal. If they differ, SCALE alone won't work — and that's almost always the trap being set.
10. What scale factor should be applied to the rectangle?
    Answer: Apply a scale factor of $1.5$. When scaling an object in AutoCAD, it's critical to understand that area scales by the square of the linear scale factor. So if you apply a scale factor of $k$, the new area equals the original area multiplied by $k^2$. This means you can't simply divide the new area by the old area to find your scale factor — that gives you the area ratio, not the linear scale factor. Here's how to work it correctly. First, find the area ratio: $\frac{108}{48} = 2.25$. This tells you the area must increase by a factor of $2.25$. Since area scales as $k^2$, you need to take the square root to find the linear scale factor: $k = \sqrt{2.25} = 1.5$. That confirms C is correct — applying a scale factor of $1.5$ in AutoCAD will produce a rectangle with $48 \times 1.5^2 = 48 \times 2.25 = 108$ square units. Looking at the distractors: A ($0.6667$) would actually shrink the object, reducing the area below 48 — the opposite of what's needed. B ($1.25$) is a plausible-looking number but doesn't produce the correct result: $48 \times 1.25^2 = 75$, not 108. D ($2.25$) is the area ratio itself — this is the most tempting trap, because students who skip the square root step land here. A reliable memory tip: area problems require a square root, volume problems require a cube root. Whenever a question gives you two areas and asks for a scale factor, always compute the ratio first, then take the square root.

Start this quiz