Question

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

Explanation:

1. Recall the rule for a 180 - degree counter - clockwise rotation about the origin:

• The rule for rotating a point \((x,y)\) 180 degrees counter - clockwise about the origin is \((x,y)\to(-x,-y)\). First, we need to determine the coordinates of point \(X\). Assume the coordinates of point \(X\) are \((x_0,y_0)\).
• From the graph, if we assume the coordinates of point \(X\) are \((4, - 9)\) (by observing its position on the \(x\) and \(y\) axes).

1. Apply the rotation rule:

• According to the rule \((x,y)\to(-x,-y)\), when \(x = 4\) and \(y=-9\), we have \(-x=-4\) and \(-y = 9\).

Answer:

The coordinates of the image of point \(X\) are \((-4,9)\)