Question

the figure below is rotated 180° clockwise. what are the coordinates of the image of point a after this transformation?

Explanation:

1. First, identify the coordinates of point A:

• Assume the coordinates of point A are \((x,y)\). From the graph, if we estimate the position of point A, it seems to be around \(( - 8,-8)\).

1. Then, use the rule for a \(180^{\circ}\) - clock - wise rotation about the origin:

• The rule for a \(180^{\circ}\) rotation (either clock - wise or counter - clockwise) about the origin \((0,0)\) for a point \((x,y)\) is \((x,y)\to(-x,-y)\).
• For point A with coordinates \(( - 8,-8)\), when we apply the \(180^{\circ}\) rotation rule:
• \(x=-8\), \(y = - 8\). After rotation, the new \(x\) - coordinate is \(-(-8)=8\), and the new \(y\) - coordinate is \(-(-8)=8\).

Answer:

\((8,8)\)