Question

1. In the diagram, AA'B'C' is an image of AABC. Which rule describes this translation?
O(x, y) → (x-5,y-3)
O(x, y) + (x + 5, y + 3)
O(x,y) → (x-3, y-5)
O(x, y) (x+3, y + 5)

Answer 1

Option B: $(x, y) \rightarrow(x+5, y+3)$ is the rule for the translation

Explanation:

The coordinates of A,B,C are $(-3,2)$ ,$(-3,-3)$ , $(0,-2)$

The coordinates of A',B',C' are $(2,5)$ , $(2,0)$ , $(5,1)$

We need to determine the rule for the translation

The rule for the translation is given by

$P(x, y) \rightarrow P^{\prime}(x+a, y+b)$

Let us determine the translation from A to A'

$A(-3,2)\rightarrow A^{\prime}(-3+a, 2+b)\rightarrow A'(2,5)$

Thus, we have,

$\begin{aligned}-3+a &=2 \\a &=5\end{aligned}$   and   $\begin{array}{r}2+b=5 \\b=3\end{array}$

Thus, the rule is given by

$(x, y) \rightarrow(x+5, y+3)$

Therefore, Option B is the correct answer.