Question

challenge the vertices of pentagon vwxyz are v(4,5), w(6,5), x(6,7), 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. compare vwxyz and vwxyz. choose the correct graph below a. image b. image c. image

Explanation:

Step1: Find translated V'

Original $V(4,5)$. Translation: 10 left, 2 down.
New coordinates: $V'(4-10, 5-2) = (-6, 3)$

Step2: Calculate distance V to V'

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

Step3: Verify correct graph

Original pentagon has points in the first quadrant. Translating 10 left and 2 down moves the figure to the left of the y-axis, matching Option A.

Answer:

A. The correct graph is Option A, and the distance between V and V' is $\sqrt{104}$ units (or ~10.2 units)