PSAT Math : Geometry

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #527 : Geometry

Whast line goes through the points  and ?

Possible Answers:

Correct answer:

Explanation:

Let P_{1}=(1,3) and P_{2}=(7,5)

The slope is geven by:  m = (y_{2} - y_{1}) \div (x_{2} - x_{1})  so

Then we use the slope-intercept form of an equation;   so

And we convert 

 

to standard form.

Example Question #21 : Geometry

What is the equation of the line that passes through the points (4,7) and (8,10)?

Possible Answers:

Correct answer:

Explanation:

In order to find the equation of the line, we will first need to find the slope between the two points through which it passes. The slope, , of a line that passes through the points and is given by the formula below:

We are given our two points, (4,7) and (8,10), allowing us to calculate the slope.

Next, we can use point slope form to find the equation of a line with this slope that passes through one of the given points. We will use (4,7).

Multiply both sides by four to eliminate the fraction, and simplify by distribution.

Subtract from both sides and add twelve to both sides.

This gives our final answer:

Example Question #11 : How To Find The Equation Of A Line

Which line contains the following ordered pairs:

 and

Possible Answers:

\small y=x+14

\small y=-x+14

\small y=-\frac{1}{4}x+\frac{7}{2}

\small y=\frac{1}{4}x+\frac{7}{2}

Correct answer:

\small y=-\frac{1}{4}x+\frac{7}{2}

Explanation:

First, solve for slope.

\small m=\frac{\Delta y}{\Delta x}=\frac{2-4}{6-(-2)}=\frac{-2}{8}=-\frac{1}{4}

Then, substitute one of the points into the equation y=mx+b.

\small 2=(-\frac{1}{4})(6)+b

\small 2=(-\frac{3}{2})+b

\small b=2+\frac{3}{2}=\frac{7}{2}

This leaves us with the equation \small y=-\frac{1}{4}+\frac{7}{2}

Example Question #21 : Psat Mathematics

Axes

Refer to the above red line. What is its equation in standard form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

 

Since we are looking for standard form - that is,  - we do the following:

 

or 

Example Question #21 : Psat Mathematics

Axes

Refer to the above red line. What is its equation in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

 

Example Question #23 : Psat Mathematics

Axes

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 3, which is .

Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us.  We set 

, and solve for  in:

Substitute for  and  in the slope-intercept form, and the equation is

Example Question #141 : Lines

Find the equation of the line shown in the graph below:

 

 Sat_math_164_05

 
Possible Answers:

 y = -1/2x + 4

y = x/2 + 4

y = -1/2x + 4

y = 2x + 4

Correct answer:

y = x/2 + 4

Explanation:

Based on the graph the y-intercept is 4. So we can eliminate choice y = x/2 - 4.

The graph is rising to the right which means our slope is positive, so we can eliminate choice y = -1/2x + 4.

Based on the line, if we start at (0,4) and go up 1 then 2 to the right we will be back on the line, meaning we have a slope of  (1/2).

Using the slope intercept formula we can plug in y= (1/2)x + 4.

 

 

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

In the xy -plane, line is given by the equation 2x - 3y = 5. If line passes through the point (a ,1), what is the value of a ?

Possible Answers:
-2
3
4
-1
5
Correct answer: 4
Explanation:

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for and solve for x:

2x - 3(1) = 5

2x - 3 = 5

2x = 8

x = 4. So the missing x-value on line l is 4.

Example Question #1 : Points And Distance Formula

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Possible Answers:

(-2,7)

(4,7)

(4,-7)

(-4,7)

(2,7)

Correct answer:

(4,7)

Explanation:

Test the difference combinations out starting with the most repeated number.  In this case, y = 7 appears most often in the answers.  Plug in y=7 and solve for x.  If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

Example Question #1 : Other Lines

Which of the following lines contains the point (8, 9)?

Possible Answers:

\dpi{100} \small 3x+6=2y

\dpi{100} \small 8x+9=y

\dpi{100} \small 3x+6=y

\dpi{100} \small 8x=9y

\dpi{100} \small 3x-6=2y

Correct answer:

\dpi{100} \small 3x-6=2y

Explanation:

In order to find out which of these lines is correct, we simply plug in the values \dpi{100} \small x=8 and \dpi{100} \small y=9 into each equation and see if it balances.

The only one for which this will work is \dpi{100} \small 3x-6=2y

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