Question

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

Explanation:

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

• The rule for rotating a point \((x,y)\) \(180^{\circ}\) clock - wise about the origin is \((x,y)\to(-x,-y)\).
• First, we need to determine the coordinates of point \(Y\). By observing the graph, assume the coordinates of point \(Y\) are \((- 6,-8)\).

1. Apply the rotation rule:

• For the \(x\) - coordinate of the image of point \(Y\): If the original \(x=-6\), after a \(180^{\circ}\) clock - wise rotation, the new \(x\) - coordinate is \(-(-6) = 6\).
• For the \(y\) - coordinate of the image of point \(Y\): If the original \(y = - 8\), after a \(180^{\circ}\) clock - wise rotation, the new \(y\) - coordinate is \(-(-8)=8\).

Answer:

The coordinates of the image of point \(Y\) are \((6,8)\).