Question

triangle xyz is shown on the coordinate plane.
if triangle xyz is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x - axis to create triangle xyz, what is the location of z?
(2, -8)
(6, -2)
(8, -2)
(12, -6)

Explanation:

Step1: Identify Z's original coordinates

From the graph, $Z = (4, -1)$

Step2: Apply translation rule $(x,y)\to(x+2,y+3)$

$x' = 4 + 2 = 6$, $y' = -1 + 3 = 2$
Translated $Z' = (6, 2)$

Step3: Reflect across x-axis $(x,y)\to(x,-y)$

$x'' = 6$, $y'' = -2$
Final $Z'' = (6, -2)$

Answer:

(6, -2)