Question

a sequence of rigid motions was performed on △abc that maps to △rst. which transformation maps △abc onto △rst? a rotate △abc 90° clockwise about point c b translate △abc 7 units to the right and 3 units down c rotate △abc90° clockwise about the origin d translate △abc 2 units to the right and 2 units down

Explanation:

Step1: Analyze rotation

Rotation about point \(C\) would change the orientation of \(\triangle ABC\) relative to \(C\). But from the grid, we can see that the relative position of the vertices with respect to each other (in terms of rotation) is not about point \(C\) as per option \(A\).

Step2: Analyze translation

Translation only moves the figure without rotation. Option \(B\) has translation values that do not match the movement from \(\triangle ABC\) to \(\triangle RST\) when we count the units on the grid. Option \(D\) also has incorrect translation values.

Step3: Analyze rotation about origin

When we rotate a point \((x,y)\) \(90^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\). By checking the coordinates of the vertices of \(\triangle ABC\) (e.g., assume \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\)) and comparing with the vertices of \(\triangle RST\) after applying the \(90^{\circ}\) clock - wise rotation about the origin rule, we can verify.

Answer:

C. rotate \(\triangle ABC\) \(90^{\circ}\) clockwise about the origin