SAT Math - 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?

(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).

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)

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.

$\overline{AB}$ 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).

The two endpoints of a line segment are and . Find the midpoint.

Explanation

In order to find the midpoint of a line segment, you need to average the x and y values of the endpoints.

The midpoint formula is

$((x_{1}+x_{2})/2), ((y_{1}+y_{2})/2)$

After plugging in the values you get

for x

and for y

Therefore, the midpoint is at .

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 $(3,16)$ .

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

Find the midpoint of a line segment with end points (1,3) and (11,3).

Explanation

To solve, simply realize you are on a horizantal line, so you just need to find the distance betweent he two x coordants and find half way between them. Thus,