# Geometry: Coordinate Shapes (3)

In this worksheet, students work out the coordinates of the missing corner of a rectangle, given the other three corners.

Key stage:  KS 2

Curriculum topic:   Geometry: Position and Direction

Curriculum subtopic:   Know, Describe and Present Shapes

Difficulty level:

### QUESTION 1 of 10

It is possible to work out the coordinates of a missing corner of a rectangle given the coordinates of the other three corners.

Example

Three of the corners of a rectangle are at (4,2), (8,2) and (4,8).

Find the coordinates of the fourth corner.

(4, 2) and (8, 2) are the base points because the y-coordinate is 2 compared to (4, 8).

The missing point must have its y-coordinate at 8 also.

(4, 2) and (8, 2) have x-coordinates which differ by 4, so the missing point must have its x-coordinate 4 more than (4,8).....i.e. 4 + 4 = 8.

The missing point has coordinates (8, 8).

Three of the corners of a rectangle are at (3,2), (8,2) and (3,8).

Find the coordinates of the fourth corner.

(2, 4)

(2, 8)

(8, 8)

(8, 4)

Three of the corners of a rectangle are at (4,3), (8,3) and (4,6).

Find the coordinates of the fourth corner.

(8, 6)

(6, 8)

(4, 8)

(2, 8)

Three of the corners of a rectangle are at (4,2), (5,2) and (5,8).

Find the coordinates of the fourth corner.

(6, 8)

(2, 6)

(8, 6)

(4, 8)

Three of the corners of a rectangle are at (4,7), (7,2) and (7,7).

Find the coordinates of the fourth corner.

(4, 2)

(8, 7)

(7, 4)

(2, 7)

Three of the corners of a rectangle are at (6,2), (8,2) and (6,10).

Find the coordinates of the fourth corner.

(7, 6)

(7, 7)

(8, 10)

(8, 6)

Three of the corners of a rectangle are at (7,2), (8,2) and (7,10).

Find the coordinates of the fourth corner.

(7, 6)

(7, 7)

(8, 10)

(8, 6)

Three of the corners of a rectangle are at (0,2), (6,2) and (6,10).

Find the coordinates of the fourth corner.

(2, 6)

(0, 10)

(8, 10)

(10, 6)

Three of the corners of a rectangle are at (1,2), (10,2) and (1,10).

Find the coordinates of the fourth corner.

(2, 6)

(10, 10)

(8, 10)

(10, 6)

Three of the corners of a rectangle are at (1,2), (20,2) and (1,10).

Find the coordinates of the fourth corner.

(2, 6)

(10, 10)

(20, 10)

(10, 6)

Three of the corners of a rectangle are at (1,2), (200,2) and (1,10).

Find the coordinates of the fourth corner.

(2, 6)

(10, 200)

(20, 10)

(200, 10)

• Question 1

Three of the corners of a rectangle are at (3,2), (8,2) and (3,8).

Find the coordinates of the fourth corner.

(8, 8)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 5, so the missing corner must have an x-coordinate 3 + 5 = 8. The y-coordinate for one corner is 8, whilst the other corners are 2, so the missing y-coordinate must be 8. Missing corner: (8, 8)
• Question 2

Three of the corners of a rectangle are at (4,3), (8,3) and (4,6).

Find the coordinates of the fourth corner.

(8, 6)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 4, so the missing corner must have an x-coordinate 4 + 4 = 8. The y-coordinate for one corner is 6, whilst the other corners are 3, so the missing y-coordinate must be 6. Missing corner: (8, 6)
• Question 3

Three of the corners of a rectangle are at (4,2), (5,2) and (5,8).

Find the coordinates of the fourth corner.

(4, 8)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 1, so the missing corner must have an x-coordinate 5 - 1 = 4. The y-coordinate for one corner is 8, whilst the other corners are 2, so the missing y-coordinate must be 8. Missing corner: (4, 8)
• Question 4

Three of the corners of a rectangle are at (4,7), (7,2) and (7,7).

Find the coordinates of the fourth corner.

(4, 2)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 3, so the missing corner must also have an x-coordinate 7 - 3 = 4. The y-coordinates for two corners is 7, whilst one of the corners the y-coordinate is 2, so the missing y-coordinate must be 2. Missing corner: (4, 2)
• Question 5

Three of the corners of a rectangle are at (6,2), (8,2) and (6,10).

Find the coordinates of the fourth corner.

(8, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 2, so the missing corner must also have an x-coordinate 6 + 2 = 8. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (8, 10)
• Question 6

Three of the corners of a rectangle are at (7,2), (8,2) and (7,10).

Find the coordinates of the fourth corner.

(8, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 1, so the missing corner must also have an x-coordinate 7 + 1 = 8. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (8, 10)
• Question 7

Three of the corners of a rectangle are at (0,2), (6,2) and (6,10).

Find the coordinates of the fourth corner.

(0, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 0, so the missing corner must also have an x-coordinate 6 - 6 = 0. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (0, 10)
• Question 8

Three of the corners of a rectangle are at (1,2), (10,2) and (1,10).

Find the coordinates of the fourth corner.

(10, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 9, so the missing corner must also have an x-coordinate 1 + 9 = 10. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (10, 10)
• Question 9

Three of the corners of a rectangle are at (1,2), (20,2) and (1,10).

Find the coordinates of the fourth corner.

(20, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 19, so the missing corner must also have an x-coordinate 1 + 19 = 20. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (20, 10)
• Question 10

Three of the corners of a rectangle are at (1,2), (200,2) and (1,10).

Find the coordinates of the fourth corner.

(200, 10)
EDDIE SAYS
The x-coordinates of the first two corners have a difference of 199, so the missing corner must also have an x-coordinate 1 + 199 = 200. The y-coordinate for one corner is 10, whilst the other corners are 2, so the missing y-coordinate must be 10. Missing corner: (200, 10)
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