### All PSAT Math Resources

## Example Questions

### Example Question #1 : Midpoint Formula

A line segment has endpoints (0,4) and (5,6). What are the coordinates of the midpoint?

**Possible Answers:**

(2.5,-5)

(2.5,5)

(0,6)

(0,4)

(3,9)

**Correct answer:**

(2.5,5)

A line segment has endpoints (0,4) and (5,6). To find the midpoint, use the midpoint formula:

X: (x_{1}+x_{2})/2 = (0+5)/2 = 2.5

Y: (y_{1}+y_{2})/2 = (4+6)/2 = 5

The coordinates of the midpoint are (2.5,5).

### Example Question #1 : Midpoint Formula

Find the midpoint between (-3,7) and (5,-9)

**Possible Answers:**

(4,-8)

(-1,-1)

(4,-1)

(1,-8)

(1,-1)

**Correct answer:**

(1,-1)

You can find the midpoint of each coordinate by averaging them. In other words, add the two x coordinates together and divide by 2 and add the two y coordinates together and divide by 2.

x-midpoint = (-3 + 5)/2 = 2/2 = 1

y-midpoint = (7 + -9)/2 = -2/2 = -1

(1,-1)

### Example Question #1 : How To Find The Midpoint Of A Line Segment

Find the coordinates for the midpoint of the line segment that spans from (1, 1) to (11, 11).

**Possible Answers:**

(6, 6)

(7, 7)

(5, 5)

(6, 5)

(5, 6)

**Correct answer:**

(6, 6)

The correct answer is (6, 6). The midpoint formula is ((x_{1 }+ x_{2})/2),((y_{1 }+ y_{2})/2) So 1 + 11 = 12, and 12/2 = 6 for both the x and y coordinates.

### Example Question #2 : Midpoint Formula

What is the midpoint between the points (–1, 2) and (3, –6)?

**Possible Answers:**

(1,2)

(1,–2)

(–1,2)

(3,1)

(–2,–1)

**Correct answer:**

(1,–2)

midpoint = ((x_{1} + x_{2})/2, (y_{1} + y_{2})/2)

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)

### Example Question #1 : How To Find The Midpoint Of A Line Segment

A line segment connects the points and . What is the midpoint of this segment?

**Possible Answers:**

**Correct answer:**

To solve this problem you will need to use the midpoint formula:

Plug in the given values for the endpoints of the segment: and .

### Example Question #4 : How To Find The Midpoint Of A Line Segment

What is the midpoint between and ?

**Possible Answers:**

**Correct answer:**

The midpoint is the point halfway between the two endpoints, so sum up the coordinates and divide by 2:

### Example Question #1 : Midpoint Formula

has endpoints and .

What is the midpoint of ?

**Possible Answers:**

**Correct answer:**

The midpoint is simply the point halfway between the x-coordinates and halfway between the y-coordinates:

Sum the x-coordinates and divide by 2:

Sum the y-coordinates and divide by 2:

Therefore the midpoint is (5.5, 6.5).

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