Where can mirror lines go?

Mirror lines can go anywhere.

The mirror line can be placed anywhere just reflect

Where are the mirror lines?

Remember the formula for a straight line is:

$y=mx+c$

(you must see and learn the section on straight lines before you proceed.)

Verticle lines

Example

Draw a reflection of the following image with a mirror line on $x=3$ .

Reflect this image so it mirrors vertically

NOTE:

For $x=3$ we can work out that if:

$y=1$ then $x=3$

$y=2$ then $x=3$

$y=3$ then $x=3$ etc

If we plot this on our graph we can find the mirror line.

Draw the mirror line vertically so it goes through the x axis but parallel with the Y axis

We can now complete the reflection.

Complete the reflection through the mirror line

Horizontal lines

Example

Draw a reflection of the following image with a mirror line on $y=4$ .

Reflect this image so it mirrors horizontally

NOTE:

For $y=4$ we can work out that if:

$x=5$ then $y=4$

$x=4$ then $y=4$

$x=3$ then $y=4$ etc

If we plot this on our graph we can find the mirror line.

Draw the mirror line through the Y axis so it is parallel with the x axis

We can now complete the reflection.

Complete the reflection through the mirror line

Diagonal lines

Example 1

Draw a reflection of the following image with a mirror line on $y=x$ .

Reflect this image so it mirrors diagonally

NOTE:

For $y=x$ we can work out that if:

$y=1$ then $x=1$

$y=2$ then $x=2$

$y=3$ then $x=3$ etc

If we plot this on our graph we can find the mirror line.

Draw a line through the intersection of both axis this is the diagonal mirror line

We can now complete the reflection.

Complete the reflection through the mirror line

Example 2

Draw a reflection of the following image with a mirror line $y=-x$ .

Reflect this shape diagonally

NOTE:

For $y=-x$ we can work out that if:

$y=1$ then $x=-1$ $(1=-1timesx$ therefore $x=-1)$

$y=2$ then $x=-2$

$y=3$ then $x=-3$ etc

If we plot this on our graph we can find the mirror line.

Draw the mirror line through Y -x

We can now complete the reflection.

Complete the reflection through the mirror line

Other examples

Example 1

On the grid below reflect the triangle in the line A, B.

Reflect this image where the mirror line goes through the shape

Redraw as follows:

Measure and reflect through the shape as normal

Example 2

Describe the single transformation that maps A to B.

Describe this reflection

You must first describe what this is and it is a REFLECTION.

You must now find the mirror line.

This is easy because we can describe this as a mirror line along the $x$ axis.

If you want to get technical, it is the line $y=0$ .

i.e. $x=1$ then $y=0$

$x=2$ then $y=0$

$x=3$ then $y=0$ etc

Answer:

This is a reflection where the mirror line is on the $x$ axis.