Question

A triangle has vertices A (0,0) B (2,6) and (0,4) Rotate it 180 clock wise about the origin followed by a dilation with a scale factor of 3 find the coordinates of the vertices of A’ B’ C’ and state whether the two triangles are congruent or similar

Answer 1

9514 1404 393

Answer:

• A'(0, 0), B'(-6, -18), C'(0, -12)

Explanation:

Rotation 180° is the transformation ...

(x, y) ⇒ (-x, -y)

Dilation by a factor of 3 is the transformation ...

(x, y) ⇒ (3x, 3y)

The two transformations together can be described by ...

(x, y) ⇒ (-3x, -3y)

That is, the coordinates of A, B, C are each multiplied by -3. The image vertices are ...

A' = -3A = A'(0, 0) . . . . . . . . the center of rotation and dilation is invariant

B' = -3B = B'(-6, -18)

C' = -3C = C'(0, -12)

Any dilated figure will not be congruent to the original. The triangles are similar.