PSAT Math : How to find the midpoint of a line segment

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

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

Possible Answers:

(2.5,5)

(3,9)

(0,6)

(0,4)

(2.5,-5)

Correct answer:

(2.5,5)

Explanation:

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

X: (x1+x2)/2 = (0+5)/2 = 2.5 

Y: (y1+y2)/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:

(-1,-1)

(1,-8)

(4,-1)

(4,-8)

(1,-1)

Correct answer:

(1,-1)

Explanation:

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 #2 : 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)

(5, 6)

(6, 5) 

(7, 7) 

(5, 5)

Correct answer:

(6, 6)

Explanation:

The correct answer is (6, 6). The midpoint formula is ((x+ x2)/2),((y+ y2)/2) So 1 + 11 = 12, and 12/2 = 6 for both the x and y coordinates.

Example Question #2 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

(1,–2)

(–1,2)

(1,2)

(–2,–1)

(3,1)

Correct answer:

(1,–2)

Explanation:

midpoint = ((x1 + x2)/2, (y1 + y2)/2)

             = ((–1 + 3)/2, (2 – 6)/2)

             = (2/2, –4/2)

             = (1,–2)

Example Question #3 : How To Find The Midpoint Of A Line Segment

A line segment connects the points (-1,4) and (3,16). What is the midpoint of this segment?

Possible Answers:

(1,10)

(0,6)

(-1,6)

(2,10)

(2,5)

Correct answer:

(1,10)

Explanation:

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

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

Plug in the given values for the endpoints of the segment: (-1,4) and (3,16).

midpoint = (\frac{-1+3}{2},\frac{4+16}{2} ) = (\frac{2}{2}, \frac{20}{2}) = (1, 10)

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

What is the midpoint between  and ?

Possible Answers:

Correct answer:

Explanation:

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

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

 has endpoints  and

What is the midpoint of

Possible Answers:

Correct answer:

Explanation:

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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