Question

apply your knowledge of dilations on the coordinate plane to answer 8 - 10.

1. the coordinates of triangle xyz are given below. adeline is going to dilate the triangle using the rule (x,y)→(\\(\frac{5}{3}x,\frac{5}{3}y\\)).

x(6,3) y(9,9) z(9,12)
a. will xyz be larger or smaller than xyz?
b. find the location of z.

1. max wrote the rule (x,y)→(5x,5y) to represent the dilation below. is maxs rule correct? explain.

Explanation:

Step1: Analyze the dilation factor

The dilation rule is $(x,y)\to(\frac{5}{3}x,\frac{5}{3}y)$. Since the scale factor $\frac{5}{3}> 1$, the new triangle will be larger.

Step2: Find the coordinates of $Z'$

The coordinates of $Z$ are $(9,12)$. Using the dilation rule $(x,y)\to(\frac{5}{3}x,\frac{5}{3}y)$, for $x = 9$ and $y=12$, we have $x'=\frac{5}{3}\times9 = 15$ and $y'=\frac{5}{3}\times12=20$. So the coordinates of $Z'$ are $(15,20)$.

Answer:

a. Larger
b. $(15,20)$