6.3 Geometry  (Page 6/7)

Discussion : translation of a point horizontally

Complete the table, by filling in the co-ordinates of the points shown in the figure.

What do you notice about the $x$ co-ordinates? What do you notice about the $y$ co-ordinates?

What would happen to the co-ordinates of point A, if it was moved to the position of point G?

When a point is moved horizontally left or right on the Cartesian plane, the $y$ co-ordinate of the point remains the same, but the $x$ co-ordinate changes by the amount that the point was moved left or right.

For example, in [link] Point A is moved 4 units right to the position marked by G. The new $y$ co-ordinate of point A is the same ( $y$ =1), but the new $x$ co-ordinate is shifted in the positive $x$ direction 4 units and becomes $x$ =-2 +4 =2. The new co-ordinate of point A at G is therefore (2;1). Similarly, for point B that is moved left by 5 units, the $y$ co-ordinate is the same ( $y=-2,5$ ), but the $x$ co-ordinate is shifted in the negative $x$ -direction by 5 units. The new $x$ co-ordinate is therefore $x$ =2,5 -5 =-2,5. The new co-ordinates of point B at H is therefore (-2,5;1).

Reflection of a point

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 $y=x$ .

Reflection on the $x$ -axis

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.

Reflection on the $y$ -axis

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.