Question

challenge the vertices of pentagon vwxyz are v(4,5), w(0,5), x(6,7), y(5,9), and z(4,7). graph vwxyz and vwxyz, its image after a translation 10 units left and 7 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 coordinates

Translation rule: $(x,y)\to(x-10,y-2)$

• $V(4,5)\to V'(4-10,5-2)=(-6,3)$
• $W(6,5)\to W'(6-10,5-2)=(-4,3)$
• $X(6,7)\to X'(6-10,7-2)=(-4,5)$
• $Y(5,8)\to Y'(5-10,8-2)=(-5,6)$
• $Z(4,7)\to Z'(4-10,7-2)=(-6,5)$

Step2: Match to correct graph

Original figure is in the first quadrant; translated figure shifts left 10, down 2 to the second quadrant. This matches option A.

Step3: Calculate distance $VV'$

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

Answer:

Correct graph: A
Distance between $V$ and $V'$: $\approx10.2$ units