The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Geometry: Coordinate Shapes (3)

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

'Geometry: Coordinate Shapes (3)' worksheet

Key stage:  KS 2

Curriculum topic:   Geometry: Position and Direction

Curriculum subtopic:   Know, Describe and Present Shapes

Difficulty level:  

Worksheet Overview

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.

 

Answer

(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).

 

Missing coordinates

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.

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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.

 

CORRECT ANSWER
(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)
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.