Question

question 6
10 pts
g.gsr.3.2 (mc)
if abcd is translated by the rule (x + 4, y − 3), then reflected over the x-axis, where would point d be located?
image of a coordinate grid with rectangle abcd, points: a(-5,1), b(-5,3), c(-2,3), d(-2,1)
options: (-5, -5), (-2, -2), (5, 5), (2, 2)

Explanation:

Step1: Find coordinates of D

From the graph, point D is at \((-2, 1)\).

Step2: Apply translation rule \((x + 4, y - 3)\)

For \(x\)-coordinate: \(-2 + 4 = 2\)
For \(y\)-coordinate: \(1 - 3 = -2\)
After translation, D' is at \((2, -2)\).

Step3: Reflect over x - axis

The rule for reflection over x - axis is \((x, y)\to(x, -y)\).
Applying to D' \((2, -2)\):
\(x\)-coordinate remains \(2\), \(y\)-coordinate: \(-(-2)=2\)
So D'' is at \((2, 2)\).

Answer:

D. (2, 2)