# 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:

### QUESTION 1 of 10

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).

Look at this grid.

Select the coordinates of the midpoint of AB.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of HI.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of FH.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of BC.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of EG.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of HJ.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of IB.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of AC.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of CD.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

Look at this grid.

Select the coordinates of the midpoint of FG.

(-1, -3)

(-3, -3)

(2, 1)

(-2, 5)

(-3, 4)

(-1, 1)

(4½, -3)

(-½, 3)

(1, -3)

(0, 5)

• Question 1

Look at this grid.

Select the coordinates of the midpoint of AB.

(-3, -3)
EDDIE SAYS
A to B is 4 units long Half the distance is 2 units from either end, count this and read the coordinate.
• Question 2

Look at this grid.

Select the coordinates of the midpoint of HI.

(-2, 5)
EDDIE SAYS
H to I is 2 units long Half the distance is 1 unit from either end, count this and read the coordinate.
• Question 3

Look at this grid.

Select the coordinates of the midpoint of FH.

(-3, 4)
EDDIE SAYS
F to H is 2 units long Half the distance is 1 unit from either end, count this and read the coordinate.
• Question 4

Look at this grid.

Select the coordinates of the midpoint of BC.

(1, -3)
EDDIE SAYS
B to C is 4 units long Half the distance is 2 units from either end, count this and read the coordinate.
• Question 5

Look at this grid.

Select the coordinates of the midpoint of EG.

(2, 1)
EDDIE SAYS
E to G is 4 units long Half the distance is 2 units from either end, count this and read the coordinate.
• Question 6

Look at this grid.

Select the coordinates of the midpoint of HJ.

(0, 5)
EDDIE SAYS
H to J is 6 units long Half the distance is 3 units from either end, count this and read the coordinate.
• Question 7

Look at this grid.

Select the coordinates of the midpoint of IB.

(-1, 1)
EDDIE SAYS
I to B is 4 units long Half the distance is 2 units from either end, count this and read the coordinate.
• Question 8

Look at this grid.

Select the coordinates of the midpoint of AC.

(-1, -3)
EDDIE SAYS
A to C is 8 units long Half the distance is 4 units from either end, count this and read the coordinate.
• Question 9

Look at this grid.

Select the coordinates of the midpoint of CD.

(4½, -3)
EDDIE SAYS
C to D is 3 units long Half the distance is 1.5 units from either end, count this and read the coordinate.
• Question 10

Look at this grid.

Select the coordinates of the midpoint of FG.

(-½, 3)
EDDIE SAYS
F to G is 5 units long Half the distance is 2.5 units from either end, count this and read the coordinate.
---- OR ----

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