Question

Given that a(-9, -5), state the equation of the translation.

A) a'(3, 8)
B) a'(12, 3)
C) a'(0, 0)
D) a'(6, 13)

Answer 1

To find the equation of the translation, we calculate the difference between the original point A (-9, -5) and each given option for translated point A'. Option A provides the correct translation vector (12, 13), yielding the equation x' = x + 12, y' = y + 13.

Step-by-step explanation:

To determine the equation of the translation, we need to find the difference between the coordinates of point A and its translated point A'. If point A is at (-9, -5) and we are given several options for A', we must subtract the coordinates of A from A' to see which results in a consistent translation vector.

Let's check each option for A':

1. A' (3, 8): The translation would be (3 - (-9), 8 - (-5)) = (12, 13).
2. A' (12, 3): The translation would be (12 - (-9), 3 - (-5)) = (21, 8).
3. A' (0, 0): The translation would be (0 - (-9), 0 - (-5)) = (9, 5).
4. A' (6, 13): The translation would be (6 - (-9), 13 - (-5)) = (15, 18).

Comparing these results to the given options, we see that option A provides a correct point A' with the translation (12, 13), which means the equation of the translation that moves A to A' (3, 8) is:

x' = x + 12

y' = y + 13