How to find the midpoint of a line segment

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

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1

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

(0,4)

0

(0,6)

0

(2.5,-5)

0

(2.5,5)

CORRECT

(3,9)

0

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)

CORRECT

(4,-1)

0

(1,-8)

0

(-1,-1)

0

(4,-8)

0

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)

0

(6, 5)

0

(5, 5)

0

(6, 6)

CORRECT

(7, 7)

0

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

has endpoints and .

What is the midpoint of ?

CORRECT

0

0

0

0

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).

5

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

CORRECT

0

0

0

0

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

After plugging in the values you get

for x

and for y

Therefore, the midpoint is at .

6

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

(1,10)

CORRECT

(2,5)

0

(-1,6)

0

(2,10)

0

(0,6)

0

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)

7

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

CORRECT

0

0

0

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,

Thus, the midpoint is at (1+5,3) which is (6,3).

8

What is the midpoint between and ?

CORRECT

0

0

0

0

Explanation

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

9

What is the midpoint of a line segment that begins at (0, -1) and ends at (4, 10)?

CORRECT

0

0

0

None of the given answers.

0

Explanation

The midpoint of a line segment can be found by averaging the x-values and y-values of the given ordered pairs. In other words,

.

Take the average of the given x- and y-values of our ordered pairs.

10

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

(1,2)

0

(3,1)

0

(1,–2)

CORRECT

(–1,2)

0

(–2,–1)

0

Explanation

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

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)