Everything Maths Grade 11

16.6 CHAPTER 16. GEOMETRY

Point x-coordinate y-coordinate

A B C D E F G H

F E

G H

B A

C D

� �

� �

�

� �

�

What do you notice about the x-coordinates? What do you notice about the y-coordinates?

What would happen tothe coordinates of point A, if the square ABCD was enlarged by a

factor of 2?

Activity: Enlargement of a Polygon

H

I

K J

H�

I�

K� J�

0 1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

In the figure quadrilateral HIJK has been enlarged by afactor of 2 through the origin to be-

come H�I�J�K�. Complete the following table using the information in the figure.

Co-ordinate Co-ordinate’ Length Length’

H = ( ; ) H�= ( ; ) OH = OH�=

I = ( ; ) I�= ( ; ) OI = OI�=

J = ( ; ) J�= ( ; ) OJ = OJ�=

K = ( ; ) K�= ( ; ) OK = OK�=

What conclusions can you draw about

1. the co-ordinates


2. the lengths when weenlarge by a factor of 2?

We conclude as follows:
Let the vertices of a triangle have co-ordinates S(x 1 ; y 1 ), T(x 2 ; y 2 ), U(x 3 ; y 3 ).�S�T�U�is an enlarge-
ment through the originof�ST U by a factor of c (c > 0 ).

•�ST U is a reduction of�S�T�U�by a factor of c.

•�S�T�U�can alternatively be seen as an reduction through the origin of�ST U by a factor of

1

c. (Note that a reductionby

1

cis the same as an enlargement by c).

• The vertices of�S�T�U�are S�(cx 1 ; cy 1 ), T�(cx 2 ,cy 2 ), U�(cx 3 ,cy 3 ).