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Midpoints on a Grid

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

'Midpoints on a Grid' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Use Coordinates in All Four Quadrants

Difficulty level:  

down

Worksheet Overview

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.

 

Answer

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.

CORRECT ANSWER
(-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.

CORRECT ANSWER
(-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.

CORRECT ANSWER
(-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.

CORRECT ANSWER
(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.

CORRECT ANSWER
(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.

CORRECT ANSWER
(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.

CORRECT ANSWER
(-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.

CORRECT ANSWER
(-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.

CORRECT ANSWER
(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.

CORRECT ANSWER
(-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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