Question

1. $\delta abc$ is translated using the rule below and the image of $\delta abc$ is given. find the pre image. $\delta abc$ is translated using the rule: $(x, y) \to (x +5, y - 2)$ draw the image $\delta abc$. what are the coordinates of? a $\underline{\quad\quad}$ $\to$ $a \underline{(1, 2)}$ b $\underline{\quad\quad}$ $\to$ $b \underline{(3, -3)}$ c $\underline{\quad\quad}$ $\to$ $c \underline{(-1, -3)}$

Explanation:

Step1: Reverse x-translation

To reverse $x \to x+5$, use $x_{\text{pre}} = x_{\text{image}} - 5$

Step2: Reverse y-translation

To reverse $y \to y-2$, use $y_{\text{pre}} = y_{\text{image}} + 2$

Step3: Calculate A's coordinates

For $A'(1,2)$:
$x = 1 - 5 = -4$, $y = 2 + 2 = 4$

Step4: Calculate B's coordinates

For $B'(3,-3)$:
$x = 3 - 5 = -2$, $y = -3 + 2 = -1$

Step5: Calculate C's coordinates

For $C'(-1,-3)$:
$x = -1 - 5 = -6$, $y = -3 + 2 = -1$

Answer:

A: $(-4, 4)$
B: $(-2, -1)$
C: $(-6, -1)$