  # Midpoints on a Grid

In this worksheet, students must find the coordinates of the midpoint of a horizontal or vertical line, given its endpoints. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Coordinates in All Four Quadrants

Difficulty level:   #### Worksheet Overview

This worksheet is about identifying the midpoints of a line on a coordinate grid.

The lines will be horizontal or vertical.

You will be given the endpoints of the line.

Remember the x number comes before the y number.

To find the midpoint

• Find the length of the whole line.
• Halve this length.
• Move along this half-distance from either of the endpoints.

Example

Find the coordinates of M, the midpoint of AC shown on the grid below. The line AC is 8 units long.

Count the squares to check.

A has an x-coordinate of -5.

B has an x-coordinate of +3.

From -5 up to +3 is 8 units.

The half-distance is 8 ÷ 2 = 4 units. M is the midpoint on the line AC.

It is 4 units to the right of A and 4 units to the left of C.

The coordinates of M are (-1, -3).

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