Question

visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this try this video for example 4 - translating a figure in the coordinate plane 4) graph quadrilateral abcd with vertices a(1, -2), b(2, 1), c(4, 1), and d(4, -2) and its image after the translation (x, y) → (x - 1, y + 4).

Explanation:

Step1: Apply translation to A

Substitute $A(1,-2)$ into $(x-1, y+4)$

$$\begin{aligned} x' &= 1 - 1 = 0 \\ y' &= -2 + 4 = 2 \end{aligned}$$

New vertex: $A'(0,2)$

Step2: Apply translation to B

Substitute $B(2,1)$ into $(x-1, y+4)$

$$\begin{aligned} x' &= 2 - 1 = 1 \\ y' &= 1 + 4 = 5 \end{aligned}$$

New vertex: $B'(1,5)$

Step3: Apply translation to C

Substitute $C(4,1)$ into $(x-1, y+4)$

$$\begin{aligned} x' &= 4 - 1 = 3 \\ y' &= 1 + 4 = 5 \end{aligned}$$

New vertex: $C'(3,5)$

Step4: Apply translation to D

Substitute $D(4,-2)$ into $(x-1, y+4)$

$$\begin{aligned} x' &= 4 - 1 = 3 \\ y' &= -2 + 4 = 2 \end{aligned}$$

New vertex: $D'(3,2)$

Answer:

Original quadrilateral vertices: $A(1,-2)$, $B(2,1)$, $C(4,1)$, $D(4,-2)$
Translated image vertices: $A'(0,2)$, $B'(1,5)$, $C'(3,5)$, $D'(3,2)$
(To graph: plot the original 4 points and connect them, then plot the 4 translated points and connect them on the coordinate plane.)