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

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Example Questions

Example Question #1 : Midpoint Formula

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

Possible Answers:

(0,6)

(2.5,5)

(3,9)

(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).

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

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

Possible Answers:

(1,-8)

(1,-1)

(4,-8)

(-1,-1)

(4,-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)

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Example Question #181 : Coordinate Geometry

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

Possible Answers:

(6, 5)

(5, 6)

(7, 7)

(6, 6)

(5, 5)

Correct answer:

(6, 6)

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.

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Example Question #6 : Midpoint Formula

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

Possible Answers:

(3,1)

(1,2)

(–2,–1)

(–1,2)

(1,–2)

Correct answer:

(1,–2)

Explanation:

midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)

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Example Question #1 : 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:

$(0,6)$

$(-1,6)$

$(2,10)$

$(1,10)$

$(2,5)$

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 $(3,16)$ .

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

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Example Question #2 : Midpoint Formula

What is the midpoint between (1,4) and (5,12) ?

Possible Answers:

(4,8)

(2,10)

(8,2)

(3,8)

(3,6)

Correct answer:

(3,8)

Explanation:

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

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

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

$\overline{AB}$ has endpoints A(4,1) and B(7,12) .

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

Possible Answers:

(6,5)

(5,6)

(4,12)

(6.5,5.5)

(5.5, 6.5)

Correct answer:

(5.5, 6.5)

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:

4+7=11

$11\div 2=5.5$

Sum the y-coordinates and divide by 2:

1+12=13

$13\div 2=6.5$

Therefore the midpoint is (5.5, 6.5).

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

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Midpoint Formula

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

Example Question #181 : Coordinate Geometry

Example Question #6 : Midpoint Formula

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

Example Question #2 : Midpoint Formula

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

All PSAT Math Resources

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