Question

Triangle ABC has coordinates A(3,2), B(1,6), C(5,5). The triangles is rotated 180 degrees clockwise and then translated 5 units up. What are the coordinates of C''(after both transformations have occurred)?

A. (-10, -5)
B. (-5, 0)
C. (0, -5)

Answer 1

Answer: First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Explanation: