### All PSAT Math Resources

## Example Questions

### Example Question #1 : Points And Distance Formula

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

**Possible Answers:**

**Correct answer:**4

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 *y * and solve for *x*:

2*x *- 3(1) = 5

2*x *- 3 = 5

2*x *= 8

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

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

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

Which of these points is on that line?

**Possible Answers:**

(-4,7)

(4,7)

(4,-7)

(2,7)

(-2,7)

**Correct answer:**

(4,7)

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 : How To Find Out If A Point Is On A Line With An Equation

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

**Possible Answers:**

**Correct answer:**

In order to find out which of these lines is correct, we simply plug in the values and into each equation and see if it balances.

The only one for which this will work is

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

Which point lies on this line?

**Possible Answers:**

**Correct answer:**

Test the coordinates to find the ordered pair that makes the equation of the line true:

### Example Question #1 : Points And Distance Formula

Points *D* and *E* lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points *D* and *E*?

**Possible Answers:**

**Correct answer:**

The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation

.

Therefore, you can get an equation in the line in point-slope form, which is

.

Plug in the answer options, and you will find that only the point solves the equation.

### Example Question #31 : Lines

Which of the following points is on the line given by the equation ?

**Possible Answers:**

**Correct answer:**

In order to solve this, try each of the answer choices in the equation:

For example, when we try (3,4), we find:

This does not work. When we try all the choices, we find that only (2,4) works:

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?

**Possible Answers:**

50'

30'

35'

45'

40'

**Correct answer:**

45'

AB = 10 ’

BC = AC – AB = 25’ – 10’ = 15’

CD = 2 * AB = 2 * 10’ = 20 ’

AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

What is the distance between (1, 4) and (5, 1)?

**Possible Answers:**

4

5

3

9

7

**Correct answer:**

5

Let P_{1} = (1, 4) and P_{2} = (5, 1)

Substitute these values into the distance formula:

The distance formula is an application of the Pythagorean Theorem: a^{2} + b^{2} = c^{2}

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

What is the distance of the line drawn between points (–1,–2) and (–9,4)?

**Possible Answers:**

10

√5

6

16

4

**Correct answer:**

10

The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.

### Example Question #31 : Coordinate Geometry

What is the distance between two points and ?

**Possible Answers:**

**Correct answer:**

To find the distance between two points such as these, plot them on a graph.

Then, find the distance between the units of the points, which is 12, and the distance between the points, which is 5. The represents the horizontal leg of a right triangle and the represents the vertial leg of a right triangle. In this case, we have a 5,12,13 right triangle, but the Pythagorean Theorem can be used as well.

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