Question

on the set of axes below, triangle abc and triangle def are graphed. describe a sequence of rigid motions that would map abc onto def. a 90 degree clockwise rotation about the origin, followed by a translation of (x + 1, y - 4) a 180 degree rotation about the origin, followed by a translation of (x + 2, y + 8) a reflection over the y - axis, followed by a 90 degree clockwise rotation about the origin a 90 degree counter - clockwise rotation about the origin, followed by a reflection over

Explanation:

Step1: Analyze rotation

A \(90\) - degree clockwise rotation about the origin \((x,y)\to(y, - x)\).

Step2: Analyze translation

After rotation, a translation of \((x + 1,y+4)\) is needed.

Let's assume a point \(A(x_1,y_1)\) in \(\triangle ABC\). After a \(90\) - degree clockwise rotation about the origin, the point becomes \((y_1,-x_1)\). Then after translation \((x + 1,y + 4)\), it becomes \((y_1+1,-x_1 + 4)\) which can map the points of \(\triangle ABC\) to \(\triangle DEF\)

Answer:

A \(90\) degree clockwise rotation about the origin, followed by a translation of \((x+1,y + 4)\)