<< Chapter < Page | Chapter >> Page > |
When you stand in front of a mirror your reflection is located the same distance ( $d$ ) behind the mirror as you are standing in front of the mirror.
We can apply the same idea to a point that is reflected on the $x$ -axis, the $y$ -axis and the line $y=x$ .
If a point is reflected on the $x$ -axis, then the reflection must be the same distance below the $x$ -axis as the point is above the $x$ -axis and vice-versa, as though it were a mirror image.
Find the co-ordinates of the reflection of the point P, if P is reflected on the $x$ -axis. The co-ordinates of P are (5;10).
We are given the point P with co-ordinates (5;10) and need to find the co-ordinates of the point if it is reflected on the $x$ -axis.
The point P is above the $x$ -axis, therefore its reflection will be the same distance below the $x$ -axis as the point P is above the $x$ -axis. Therefore, $y$ =-10.
For a reflection on the $x$ -axis, the $x$ co-ordinate remains unchanged. Therefore, $x$ =5.
The co-ordinates of the reflected point are (5;-10).
If a point is reflected on the $y$ -axis, then the reflection must be the same distance to the left of the $y$ -axis as the point is to the right of the $y$ -axis and vice-versa.
Find the co-ordinates of the reflection of the point Q, if Q is reflected on the $y$ -axis. The co-ordinates of Q are (15;5).
We are given the point Q with co-ordinates (15;5) and need to find the co-ordinates of the point if it is reflected on the $y$ -axis.
The point Q is to the right of the $y$ -axis, therefore its reflection will be the same distance to the left of the $y$ -axis as the point Q is to the right of the $y$ -axis. Therefore, $x$ =-15.
For a reflection on the $y$ -axis, the $y$ co-ordinate remains unchanged. Therefore, $y$ =5.
The co-ordinates of the reflected point are (-15;5).
The final type of reflection you will learn about is the reflection of a point on the line $y=x$ .
Study the information given and complete the following table:
Point | Reflection | |
A | (2;1) | (1;2) |
B | (- $1\frac{1}{2}$ ;-2) | (-2;-1 $\frac{1}{2}$ ) |
C | (-1;1) | |
D | (2;-3) |
Notification Switch
Would you like to follow the 'Siyavula textbooks: grade 10 maths [caps]' conversation and receive update notifications?