18. Triangle CAT is located at C (-2, 2), A (4, -2), T (1, 1). Find the coordinates of its image after a dilation with a scale factor of 4. (3 points)

The coordinates of the image of triangle CAT located at C(-2, 2), A(4, -2), T (1, 1) after a dilation with a scale factor of 4 are:[tex]C'(-8,8) \\ \\ A'(16,-8) \\ \\ T'(4,4)[/tex]Explanation:In this case, we have a triangle CAT that is located at the following points:[tex]C (-2, 2) \\ \\ A (4, -2) \\ \\  T (1, 1)[/tex]When dilating objects we enlarge or reduce the size of the object. The scale factor tells us how much larger or smaller the object will become.  For a scale factor greater than 1, the object will increase in size and for a scale factor less than 1, the object will decrease in size meaning that the resulting object will be similar to the original one. So, for a point P and scale factor k, the image will be P':[tex]P(x,y) \rightarrow P'(kx,ky)[/tex] Here we'll assume the center of the dilation at the origin, so the coordinates of its image after a dilation with a scale factor of 4 are:[tex]Let's \ call \ k \ the \ scale \ factor, \ and \ C',T',A' \ the \ coordinates \ of \\ the \ image, \ so: \\ \\ k=4 \\ \\ \\ C(-2, 2) \rightarrow C'(-2\times4,2\times 4) \therefore C'(-8,8) \\ \\ A(4, -2) \rightarrow A'(4\times4,-2\times 4) \therefore A'(16,-8) \\ \\ T(1,1) \rightarrow T'(1\times4,1\times 4) \therefore T'(4,4)[/tex]Learn more:Dilation: