Question

Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.

C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)

Answer 1

To dilate a triangle using a scale factor of 3.5, we multiply the distance between each vertex and the center of dilation (in this case, the origin) by 3.5.

Using this information, we can find the coordinates of each vertex of triangle A'B'C':

A' = (43.5, 33.5) = (14, 10.5)

B' = (33.5, -23.5) = (10.5, -7)

C' = (-33.5, 13.5) = (-10.5, 3.5)

Therefore, the vertex of point C' is (-10.5, 3.5).

So the correct answer is C′(−10.5, 3.5).