How to find the midpoint of a line segment

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

Questions 1 - 7

1

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

(0,4)

(0,6)

(2.5,-5)

(2.5,5)

(3,9)

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).

2

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

(1,-1)

(4,-1)

(1,-8)

(-1,-1)

(4,-8)

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)

3

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

(5, 6)

(6, 5)

(5, 5)

(6, 6)

(7, 7)

Explanation

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.

4

$\overline{AB}$ has endpoints and .

What is the midpoint of $\overline{AB}$ ?

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:

$11\div 2=5.5$

Sum the y-coordinates and divide by 2:

$13\div 2=6.5$

Therefore the midpoint is (5.5, 6.5).

5

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

$(1,10)$

$(2,5)$

$(-1,6)$

$(2,10)$

$(0,6)$

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 $(3,16)$ .

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

6

What is the midpoint between and ?

Explanation

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

$(\frac{1+5}{2},\frac{4+12}{2})=(\frac{6}{2},\frac{16}{2})=(3,8)$

7

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

(1,2)

(3,1)

(1,–2)

(–1,2)

(–2,–1)

Explanation

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

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)

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