Question

What are the coordinates of the points V''W'' after applying the two successive translations to the line segment VW with endpoints V(-6, -4) and W(-3, 1)?

A) V''(-9, -3) and W''(-6, 2)
B) V''(3, 5) and W''(6, 0)
C) V''(-3, 0) and W''(0, 5)
D) V''(9, 3) and W''(6, -4)

Answer 1

The coordinates of the points V''W'' after applying the two successive translations to the line segment VW are V''(-9, -7) and W''(-6, 2).

Step-by-step explanation:

To find the coordinates of the points V''W'' after applying the two successive translations to the line segment VW, we need to perform each translation step by step.

The first translation from V to V'' is determined by adding the x- and y-coordinates of the translation vector (-3, -3) to the coordinates of V. This gives us V''(-6 + (-3), -4 + (-3)) = V''(-9, -7).

The second translation from V'' to V'''' is determined by adding the x- and y-coordinates of the translation vector (3, 9) to the coordinates of V''. This gives us V''''(-9 + 3, -7 + 9) = V''''(-6, 2).