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

Card 0 of 7

Question

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

Answer

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).

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Question

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

Answer

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)

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Question

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

Answer

The correct answer is (6, 6). The midpoint formula is ((x1 + x2)/2),((y1 + y2)/2) So 1 + 11 = 12, and 12/2 = 6 for both the x and y coordinates.

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Question

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

Answer

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

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)

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Question

has endpoints and .

What is the midpoint of ?

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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Question

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

Answer

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)

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Question

What is the midpoint between and ?

Answer

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

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