Midpoint of a Line Segment Worksheet

Grade 12 Math worksheet on finding the midpoint of a line segment in a coordinate plane, including conceptual understanding and application problems.

Grade 12 Math GeometryMidpoint of a Line Segment

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Multiple ChoiceFill in the BlanksShort AnswerCustom

Standards

CCSS.MATH.CONTENT.HSA.APR.D.6CCSS.MATH.CONTENT.HSG.GPE.B.7

Topics

MathGeometryMidpoint FormulaCoordinate GeometryGrade 12

6 sections · Free to use · Printable

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Midpoint of a Line Segment

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. What is the formula for finding the midpoint (M) of a line segment with endpoints (x1, y1) and (x2, y2)?

M = ((x2 - x1)/2, (y2 - y1)/2)

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

M = (x1 + x2, y1 + y2)

M = (x2 - x1, y2 - y1)

2. The midpoint of a line segment is equidistant from which of the following?

Only one endpoint

Both endpoints

The origin

Any point on the line

3. The midpoint formula is derived from finding the of the x-coordinates and the of the y-coordinates.

4. If a line segment has one endpoint at (a, b) and its midpoint at (c, d), the other endpoint can be found using the relationship: (x2, y2) = ( , ).

5. Find the midpoint of the line segment with endpoints ( -5, 3) and (7, -1).

6. A line segment has its midpoint at (2, 5) and one endpoint at (-3, 1). Find the coordinates of the other endpoint.

7. Plot the points A(-4, 2) and B(6, -4) on the coordinate plane below. Then, calculate and plot the midpoint M of the line segment AB.

Show your calculation for the midpoint M:

8. A city planner is designing a new park. Two key landmarks are located at coordinates (10, 20) and (50, 80) on a map. The main entrance to the park should be located exactly halfway between these two landmarks. What are the coordinates of the main entrance?