﻿ Unit 7 Section 4 : Reflections

Unit 7 Section 4 : Enlargements

In this section we look at line symmetry and reflections of simple shapes, in horizontal, vertical and sloping lines. In a reflection, a point will move to a new position that will be the same distance from the mirror line, but on the other side. These distances will always be measured at right angles to the mirror line.

Example 1

Draw in the lines of symmetry for each of the following shapes:

(a)
4 lines of symmetry
(b)
1 line of symmetry

Example 2

Draw the reflection of each of the following shapes in the given mirror line.

Example 3

A triangle has corners at the points with coordinates (4, 3), (5, 6) and (3, 4).
Draw the reflection of the triangle in the:

(a) (b) x-axis y-axis line x = 6 line y = 7

Example 4

An 'L' shape has corners at the points with coordinates (1, 4), (1, 7), (2, 7), (2, 5), (3, 5) and (3, 4).
Draw the reflection of the shape in the lines:

(a) (b) y = x y = –x

Exercises

Question 1

Draw in all the lines of symmetry of the following shapes.

(a)
(b)
(c)
(d)
(e)
(f)
Question 2

Draw the reflection of each of the following shapes in the line given:

(a)
(b)
(c)
(d)
(e)
(f)
Question 3

Draw the reflections of the following shapes in the lines shown:

(a)
(b)
(c)
Question 4

Reflect the shape in the lines x = 8 and x = 11.

Question 5

Reflect the shape in the lines y = 10 , y = 5 and x = 7.

Question 6

(a)

Draw the triangle that has corners at the points with coordinates (1, 1), (4, 7) and (2, 5).

(b)

Reflect the triangle in the lines:

(i) x = 8, x = –1, y = –2
Question 7

The following diagram shows the shapes A, B, C, D and E.

Write down the equation of the mirror line for each of the following reflections:

(a) A to B B to C A to D B to E D to E C to D
Question 8

(a)

Draw the triangle which has corners at the points with coordinates (1, 4), (1, 7) and (3, 5).

(b)

Reflect this shape in the line y = x and state the coordinates of the corners of the reflected shape.

(c)

Reflect the original triangle in the line y =  x and state the coordinates of the corners of the reflected shape.

Question 9

Shape A is drawn in the following diagram.

(a)

Reflect the shape A in the line x = 6 to obtain shape B.

(b)

Reflect the shape B in the line x = 14 to obtain shape C.

(c)

Describe the translation that would take shape A straight to shape C.

Question 10

Draw the triangle with corners at the points with coordinates (1, 3), (1, 8) and (6, 8).
Reflect this triangle in the following lines:

(a)

x = 0

(b)

y = 0

(c)

y = x

(d)

y = –x

Question 11

These patterns have one or more lines of symmetry. Draw all the lines of symmetry in each pattern. You may use a mirror or tracing paper to help you.

(a)
(b)
(c)
(d)
(e)
Question 12

Nina is making Rangoli patterns. To make a pattern she draws some lines on a grid. Then she reflects them in a mirror line.

Reflect each following group of lines in its mirror line to make a pattern. You may use a real mirror or tracing paper to help you.

(a)
(b)
(c)

Now use two mirror lines to make a pattern.
First reflect the group of lines in one mirror line to make a pattern.
Then reflect the whole pattern in the other mirror line.

Question 13

(a)

Three points on this line are marked with .
Their coordinates are: (1, 1), (3, 3) and (4, 4).
Look at the numbers in the coordinates of each point.
What do you notice?

x =
(b)

The point ( ? , 14.5) is on the line.
Write down its missing coordinate.

(c)

The point is above the line.
Four points are at (10, 10), (10, 12), (12, 10) and (12, 12).
Which one of these points is above the line?

(d)

The point ( ? , 15) is above the line.
Write down a possible coordinate for the point.

Look at triangles A and B.

 Triangle A Triangle B Coordinates of (4, 3) (3, 4) Coordinates of (2, 1) (1, 2) Coordinates of (6, 2) (2, 6)
Note: Triangle A was reflected onto triangle B and the coordinates are reversed.
(e)

Elen wants to reflect the point (20, 13) in the mirror line. What point will (20,13) go to?

Question 14

Catrin shades in a shape made of five squares on a grid:

She shades in 1 more square to make a shape which has the dashed line as a line of symmetry:

(a)

On the grid opposite, shade in 1 more square to make a shape which has the dashed line as a line of symmetry.

(b)

On the grid opposite, shade in 1 more square to make a shape which has the dashed line as a line of symmetry. You may use a mirror or tracing paper to help you.

(c)

On the grid opposite, shade in 2 more squares to make a shape which has the dashed line as a line of symmetry. You may use a mirror or tracing paper to help you.

(d)

On the grid opposite, shade in 2 more squares to make a shape which has the dashed line as a line of symmetry. You may use a mirror or tracing paper to help you.