Question

the triangles can be carried onto each other by performing a rotation about one of the points. which point is the center of the rotation for the figures shown? a. b b. d c. a d. c

Explanation:

Step1: Recall the property of rotation center

The center of rotation is the fixed point around which a figure rotates. In a rotation, the distance from the center of rotation to each corresponding point of the original and rotated figure remains the same.

Step2: Analyze each point

• For point \(A\): If we rotate the triangle with right - angle at \(A\) around \(A\), the other two vertices of the triangle will move, but \(A\) itself is fixed. However, the two given triangles do not have a common vertex at \(A\) in a way that \(A\) could be the center of rotation for mapping one triangle to the other.
• For point \(B\): If we consider the transformation of one triangle to the other, the distance from \(B\) to the vertices of the first triangle and the corresponding vertices of the second triangle is not consistent with the property of rotation (the distances from the center of rotation to corresponding points should be equal).
• For point \(C\): When we rotate a figure around a point, the center of rotation is equidistant from corresponding points of the pre - image and the image. If we assume a rotation about point \(C\), we can observe that the distances from \(C\) to the vertices of the first triangle and the distances from \(C\) to the corresponding vertices of the second triangle satisfy the rotation property (corresponding points are at the same distance from \(C\)).
• For point \(D\): Similar to \(B\), the distance from \(D\) to the vertices of the first triangle and the corresponding vertices of the second triangle is not consistent with the rotation property.

Answer:

D. C