Question

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

Explanation:

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

• Step 1: Reflection over the \(y\) - axis
• The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). Let the original coordinates of point \(A\) be \((x,y)\), after reflection over the \(y\) - axis, the coordinates become \(A_1(-x,y)\).
• Step 2: Rotation \(180^{\circ}\) clock - wise
• The rule for rotating a point \((a,b)\) \(180^{\circ}\) clock - wise about the origin is \((a,b)\to(-a,-b)\). Since the point after reflection is \(A_1(-x,y)\), after rotating \(180^{\circ}\) clock - wise, the new coordinates \(A_2\) are \((x, - y)\).
• From the graph, assume the coordinates of point \(A\) are \((1,-7)\).
• After reflection over the \(y\) - axis: \((1,-7)\to(-1,-7)\).
• After rotating \(180^{\circ}\) clock - wise: \((-1,-7)\to(1,7)\).

Answer:

\((1,7)\)