Question

challenge 1 the vertices of pentagon vwxyz are v(4,5), w(6,9), x(8,7), y(5,9), and z(4,7). graph vwxyz and vwxyz, its image after a translation 10 units left and 2 units down. then use the grid lines to estimate the distance between v and v. graph vwxyz and vwxyz. choose the correct graph below a. image b. image c. image

Explanation:

Step1: Find translated V'

Translation: $(x,y)\to(x-10,y-2)$
For $V(4,5)$: $V'(4-10,5-2)=(-6,3)$

Step2: Verify graph match

Check option A: The original figure is at positive x,y; the image is shifted left 10, down 2, matching $V'(-6,3)$ and the shape's position.

Step3: Calculate distance V to V'

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d=\sqrt{(-6-4)^2+(3-5)^2}=\sqrt{(-10)^2+(-2)^2}=\sqrt{100+4}=\sqrt{104}=2\sqrt{26}\approx10.2$ units

Answer:

A.