Question

3 dilate \\( \delta x y z \\) on the coordinate plane using point \\( y ( 1 7, 1 7 ) \\) as the center of dilation and a scale factor of \\( \frac { 1 } { 3 } \\).

Explanation:

Step1: Find coordinates of \(X\) and \(Z\)

From the graph, \(X=(2,17)\) and \(Z=(17,8)\)

Step2: Use dilation formula

The formula for dilation with center \((a,b)\) and scale factor \(k\) is \((x,y)\to(a + k(x - a),b + k(y - b))\)
For point \(X=(2,17)\):

$$
LATEXBLOCK0
$$

$$
LATEXBLOCK1
$$

So \(X'\) is \((12,17)\)
For point \(Z=(17,8)\):

$$
LATEXBLOCK2
$$

$$
LATEXBLOCK3
$$

So \(Z'\) is \((17,14)\)
Point \(Y\) remains \((17,17)\) as it is the center of dilation.

Answer:

The coordinates of the dilated triangle \(\triangle X'Y'Z'\) are \(X'(12,17)\), \(Y'(17,17)\), \(Z'(17,14)\)