Question

graph quadrilateral abcd with vertices a(-4, 1), b(-3, 3), c(0, 1), and d(-2, 0) and its image after the translation (x, y) → (x + 4, y - 2).

Explanation:

Step1: Find new coordinates of A

For point $A(-4,1)$, apply the translation $(x,y)\to(x + 4,y - 2)$.
$x=-4,y = 1$. New $x=-4 + 4=0$, new $y=1-2=-1$. So $A'=(0,-1)$.

Step2: Find new coordinates of B

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

Step3: Find new coordinates of C

For point $C(0,1)$, $x = 0,y=1$. New $x=0 + 4=4$, new $y=1-2=-1$. So $C'=(4,-1)$.

Step4: Find new coordinates of D

For point $D(-2,0)$, $x=-2,y = 0$. New $x=-2+4=2$, new $y=0 - 2=-2$. So $D'=(2,-2)$.

Step5: Graph the quadrilaterals

Graph the original quadrilateral $ABCD$ with vertices $A(-4,1),B(-3,3),C(0,1),D(-2,0)$ and the translated quadrilateral $A'B'C'D'$ with vertices $A'(0,-1),B'(1,1),C'(4,-1),D'(2,-2)$ on the given grid.

Answer:

Vertices of the original quadrilateral: $A(-4,1),B(-3,3),C(0,1),D(-2,0)$; Vertices of the translated quadrilateral: $A'(0,-1),B'(1,1),C'(4,-1),D'(2,-2)$ and graph them on the grid.