Unit 3 Section 5 : Plotting Polygons

In this section we look at polygons plotted on coordinate axes, but first, we will recap the names of polygons:

Example Question

The line marked on the coordinate grid below is one side of a square:

What are the possible coordinates of the corners of the square?

There are two possible places the square could be placed:

The missing coordinates could be ( 6 , 3 ) and ( 1 , 6 ) or ( –5 , –4 ) and ( 0 , –7 )

Practice Questions

Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

(a) Two sides of a square are shown.
What are the coordinates of the corner which is not marked?

(b) Three corners of a rectangle are shown.
What are the coordinates of the fourth corner?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
In each part below two sides of a square are shown.

Write down the coordinates of the fourth corner of each square.
(a) The fourth corner is at ( , )
(b) The fourth corner is at ( , )
(c) The fourth corner is at ( , )
(d) The fourth corner is at ( , )

Question 2
In each part of the question below the coordinates of three corners of a square are given.

Find the coordinates of the other corner in each case. You may find it helpful to draw a sketch.
(a) ( 2 , –2 ), ( 2 , 3 ) and ( –3 , 3 )
The other corner of this square is at ( , )
(b) ( 2 , 3 ), ( 3 , 4 ) and ( 1 , 4 )
The other corner of this square is at ( , )
(c) ( 2 , 2 ), ( 4 , 4 ) and ( 4 , 0 )
The other corner of this square is at ( , )
(d) ( –6 , 2 ), ( –5 , –5 ) and ( 1 , 3 )
The other corner of this square is at ( , )
(e) ( –5 , –2 ), ( –2 , –1 ) and ( –1 , –4 )
The other corner of this square is at ( , )

Question 3
In each part below two sides of a rectangle are shown.

Write down the coordinates of the fourth corner of each rectangle.
(a) The fourth corner is at ( , )
(b) The fourth corner is at ( , )

Question 4
In each part of the question below the coordinates of three corners of a rectangle are given.

Find the coordinates of the other corner in each case. You may find it helpful to draw a sketch.
(a) ( –4 , 2 ), ( –4 , 1 ) and ( 6 , 1 )
The other corner of this rectangle is at ( , )
(b) ( 0 , 2 ), ( –2 , 0 ) and ( 4 , –6 )
The other corner of this rectangle is at ( , )
(c) ( –4 , 5 ), ( –2 , –1 ) and ( 1 , 0 )
The other corner of this rectangle is at ( , )
(d) ( –5 , 1 ), ( –2 , 5 ) and ( 6 , –1 )
The other corner of this rectangle is at ( , )

Question 5
The sides of an octagon are all the same length. The diagram below shows part of the octagon.
Find the coordinates of the missing corner.
( , )
Question 6
The angles between the sides of a different octagon are all equal, but the sides are different lengths.
Find the coordinates of the missing corner.
( , )
Question 7
Two corners of a square are shown on the coordinate grid below.

(a) If the third corner is at ( 7 , –1 ), where is the fourth corner?
( , )

(b) If the third corner is at ( –3 , –1 ), where is the fourth corner?
( , )

It is possible to make a different square to those above by placing the third and fourth points in two new positions.

(c) What are the coordinates which need to be plotted?
( , ) and ( , )

You have now completed Unit 3 Section 5
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Produced by A.J.Reynolds April 2011