Question

the figure below is rotated 180° clockwise and then reflected over y - axis. what are the coordinates of the image of point a after these transformations?

Explanation:

1. First, assume the coordinates of point A are \((x,y)\).

• The rule for a \(180^{\circ}\) - clock - wise rotation about the origin is \((x,y)\to(-x, -y)\). Let the coordinates of point A be \((-8,-5)\) (estimated from the graph). After a \(180^{\circ}\) clock - wise rotation about the origin, the new coordinates \(A_1\) of point A are \((8,5)\) according to the formula \((x,y)\to(-x, -y)\).

1. Then, apply the reflection rule over the y - axis.

• The rule for reflecting a point \((x,y)\) over the y - axis is \((x,y)\to(-x,y)\).
• For the point \(A_1(8,5)\), after reflecting over the y - axis, the new coordinates \(A_2\) are \((-8,5)\) according to the formula \((x,y)\to(-x,y)\).

Answer:

The coordinates of the image of point A are \((-8,5)\)