Question

1. multi - step the coordinates of the vertices of rectangle abcd are a(-4,1), b(1,1), c(1, - 2), and d(-4, - 2). find the coordinates for the image of rectangle abcd after the translation (x,y)→(x + 3,y - 2). draw the preimage and the image.

Explanation:

Step1: Apply translation to point A

For point $A(-4,1)$, use the translation $(x,y)\to(x + 3,y - 2)$.
$x=-4,y = 1$. New $x=-4 + 3=-1$, new $y=1-2=-1$. So the new coordinates of $A$ are $A'(-1,-1)$.

Step2: Apply translation to point B

For point $B(1,1)$, with $x = 1,y = 1$. New $x=1+3 = 4$, new $y=1 - 2=-1$. So the new coordinates of $B$ are $B'(4,-1)$.

Step3: Apply translation to point C

For point $C(1,-2)$, with $x = 1,y=-2$. New $x=1 + 3=4$, new $y=-2-2=-4$. So the new coordinates of $C$ are $C'(4,-4)$.

Step4: Apply translation to point D

For point $D(-4,-2)$, with $x=-4,y=-2$. New $x=-4+3=-1$, new $y=-2 - 2=-4$. So the new coordinates of $D$ are $D'(-1,-4)$.

Answer:

The coordinates of the image rectangle $A'B'C'D'$ are $A'(-1,-1),B'(4,-1),C'(4,-4),D'(-1,-4)$