Question

1. a rectangle has vertices (0,0), (4,0), (4,3), (0,3). translate it 2 units left and 5 units up. what is one of the new vertices? a) (-2,5) b) (2,5) c) (4,5) d) (2,3)

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated $a$ units left and $b$ units up, the new - point is $(x - a,y + b)$. Here $a = 2$ and $b = 5$.

Step2: Take an original vertex

Let's take the original vertex $(0,0)$.

Step3: Apply the translation

For the vertex $(0,0)$, substituting $x = 0$, $a = 2$, $y = 0$, and $b = 5$ into the translation formula $(x - a,y + b)$, we get $(0-2,0 + 5)=(-2,5)$.

Answer:

A. (-2,5)