Question

1. triangle was rotated 90 degrees counterclockwise followed by a reflection over what line to map to triangle a\b\c\? $y = x$ $y=-x$ x - axis y - axis

Explanation:

Step1: Recall rotation and reflection rules

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise, the new coordinates are \((-y,x)\).

Step2: Analyze reflection

After rotation, for the final mapping, if we consider the line \(y = -x\). The rule for reflection over the line \(y=-x\) is \((x,y)\to(-y, -x)\).
Let's assume a general point \(P(x,y)\) on the original triangle. After \(90^{\circ}\) counter - clockwise rotation \(P_1(-y,x)\). After reflection over \(y = -x\), using the formula \((a,b)\to(-b,-a)\) for reflection over \(y=-x\), if \(a=-y\) and \(b = x\), we get \(P_2(-x,y)\) which is consistent with the transformation from the rotated triangle to \(A''B''C''\) (by checking the coordinate changes of the vertices of the triangles in the graph).

Answer:

\(y=-x\)