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Unit J1 Section 1
Reflections

Reflections are obtained when you draw the image that would be obtained in a mirror.

Every point on a reflected image is always the same distance from the mirror line as the original. This is shown below.

Note

Distances are always measured at right angles to the mirror line.

Worked Examples

1

Draw the reflection of the shape in the mirror line shown.

The lines added to the diagram show how to find the position of each point after it has been reflected.

Remember that the image of each point is the same distance from the mirror line as the original.

The points can then be joined to give the reflected image.

If the construction lines have been drawn in pencil they can be rubbed out.
2

Reflect this shape in the mirror line shown in the diagram.

The lines are drawn at right angles to the mirror line. The points which form the image must be the same distance from the mirror lines as the original points. The points which were on the mirror line remain there.

The points can then be joined to give the reflected image.

Exercises

Draw a set of axes with x and y values from −5 to 5.

Plot the points with coordinates

(1, 1), (1, 5), (4, 5), (4, 3), (2, 3), (2, 1).

Join the points in that order to form a shape.

(a)
Reflect the image in the y-axis. Write down the coordinates of the corners of this shape.

(1, 1) → (, )

(1, 5) → (, )

(4, 5) → (, )

(4, 3) → (, )

(2, 3) → (, )

(2, 1) → (, )

(b)

Reflect the image obtained in (a) in the x-axis. List the coordinates of the corners.

List the points in the same order.

(, )

(, )

(, )

(, )

(, )

(, )

(c)

Reflect the image obtained in (b) in the y-axis. Describe how this shape could have been obtained directly from the original shape.

Reflect original shape in

Give in the mirror line for each reflection described.

(a)
A → B y =
(b)
B → C y =
(c)
C → D y =
(d)
A → D y =

Copy the axes and shape shown.

Draw the reflection of the shape in the y-axis.

(a)
(i)

Compare the coordinates of each shape.

(1, 0) → (, )

(2, 0) → (, )

(2, 3) → (, )

(4, 3) → (, )

(4, 4) → (, )

(1, 4) → (, )

(ii)

Describe what happens to the coordinates of a point when it is reflected in the y-axis.

x coordinates , y coordinates .

(b)

Repeat (a) using the x-axis.

(i)

(1, 0) → (, )

(2, 0) → (, )

(2, 3) → (, )

(4, 3) → (, )

(4, 4) → (, )

(1, 4) → (, )

(ii)

x coordinates , y coordinates .