What are the coordinates of the image of C'?

Question

The coordinates of a triangle are A(8,9), B(9,4), and C(7,4). The triangle is transformed so that the coordinates of its image is is transformed so that the coordinates of its image are A'(32,36), B'(36,16), and C'(?,?) The image is a dilation of the pre image. The image is transformed by a scale factor of 4. What are the coordinates of the image of C'?

Answer 1

Let's compare the pre-image and image coordinates to establish a pattern:

 

A(8,9) and A'(32,36)

 

x-coordinates:  8,32.   8 * 4 = 32

y-coordinates:  9,36.   9 * 4 = 36

 

B(9,4) and B'(36,16)

 

x-coordinates:  9,36.  9*4 = 36

y-coordinates:  4,16.  4*4 = 16.

 

The transformation is simply a multiplication of the pre-image coordinates by the scale factor, 4.

 

So, following the pattern,

C(7,4)

C'(7*4, 4*4)