Question

1. Identify the matrix transformation of ΔXYZ, which has coordinates X(−2, −2),Y(4, 1), and Z(0, 6), for a dilation by a factor of 2.5. Then identify the correct vertices of the image
2. Identify the matrix transformation of ΔFGH, which has coordinates F(0, −1),G(5, −1), and H(4, 3), for a dilation by a factor of 1/4. Then identify the correct vertices of the image

Answer 1

If dilation is about the origin, and there is no translation, rotation, or reflection involved, the matrix of image coordinates is the matrix of original coordinates multiplied by the scalar dilation factor.

1.

$2.5\left[\begin{array}{ccc}-2&4&0\\-2&1&6\end{array}\right]=\left[\begin{array}{ccc}-5&10&0\\-5&2.5&15\end{array}\right]\\\\\text{Image coordinates are X'(-5,-5), Y'(10,2.5), Z'(0,15).}$

2.

$\dfrac{1}{4}\left[\begin{array}{ccc}0&5&4\\-1&-1&3\end{array}\right]=\left[\begin{array}{ccc}0&\frac{5}{4}&1\\-\frac{1}{4}&-\frac{1}{4}&\frac{3}{4}\end{array}\right]\\\\\text{Image coordinates are F'(0, -.25), G'(1.25, -.25), H'(1, .75).}$