Question

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

Explanation:

Step1: Determine the original coordinates of point A

From the graph, assume the original coordinates of point A are \((x,y)\). Let's first find the original coordinates. Looking at the x - axis and y - axis, if we assume the non - rotated point A has coordinates \((3,0)\) (since it's on the x - axis at \(x = 3\) and \(y=0\)).

Step2: Apply the rotation rule for \(180^{\circ}\) clockwise

The rule for a \(180^{\circ}\) rotation (clockwise or counter - clockwise) about the origin \((0,0)\) is \((x,y)\to(-x,-y)\).
Substitute \(x = 3\) and \(y = 0\) into the rule: \((3,0)\to(- 3,0)\)

Answer:

\((-3,0)\)