The pentagon is translated 5 units to the left and 4 units down. What are the coordinates of C'? and how does the translated pentagon relate to the preimage

Question

(-7,-3); Congruent, different orientation
(-2,-8); Congruent, different orientation
(3,7); Congruent, same orientation
(-3,-7); Congruent, same orientation

Answer 1

To find the coordinates of C', we need to apply the translation of 5 units to the left and 4 units down to the coordinates of C.

Let's start with the original coordinates of C: (-3,1)

Applying the translation:
-3 (original x-coordinate) - 5 (units to the left) = -3 - 5 = -8
1 (original y-coordinate) - 4 (units down) = 1 - 4 = -3

Therefore, the new coordinates of C' are (-8,-3).

Looking at the given points:
(-7,-3): not the same as C' in both x and y coordinates. Different orientation.
(-2,-8): not the same as C' in both x and y coordinates. Different orientation.
(3,7): not the same as C' in both x and y coordinates. Different orientation.
(-3,-7): not the same as C' in both x and y coordinates. Different orientation.

Therefore, the translated pentagon relates to the preimage as congruent but with a different orientation.