Question

consider figures 1 and 2 on the coordinate plane.
which sequence of transformations ma
figure 1 is mapped onto figure 2 by a rotation about the origin followed by a translation of

Explanation:

Step1: Analyze the rotation

Let's assume a point \((x,y)\) in figure 1. If we rotate a point \((x,y)\) \(90^{\circ}\) clock - wise about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Analyze the translation

After rotation, assume the general form of translation. Let's consider the vertices of the triangles. Suppose a vertex of figure 1 is \((x_1,y_1)\). After \(90^{\circ}\) clock - wise rotation, it becomes \((y_1,-x_1)\). Then, if we translate \((y_1,-x_1)\) by \((h,k)\) to get the corresponding vertex of figure 2.
Let's take a sample vertex. Suppose a vertex of figure 1 is \((6,7)\). After \(90^{\circ}\) clock - wise rotation about the origin, it becomes \((7,-6)\). Then, if we translate \((7,-6)\) by \((-13,8)\) (i.e., \(x = 7-13=-6,y=-6 + 8 = 2\)).

Answer:

\(90^{\circ}\) clockwise; \((x,y)\to(x - 13,y+8)\)