Question

in the graph below, what is the line of reflection for $\triangle xyz$ and $\triangle xyz$?
a $y=2$
b $x=2$
c the $y$-axis
d the $x$-axis

Explanation:

Step1: Identify vertex coordinates

Let’s take vertices:

• $X=(4,5)$, $X'=(4,1)$
• $Y=(3,6)$, $Y'=(3,0)$
• $Z=(2,4)$, $Z'=(2,2)$

Step2: Find midpoint y-values

For reflection, the line is the midpoint of corresponding points' y-coordinates.
For $X$ and $X'$: $\frac{5+1}{2}=3$
For $Y$ and $Y'$: $\frac{6+0}{2}=3$
For $Z$ and $Z'$: $\frac{4+2}{2}=3$
Wait, correction: Recheck grid (y-axis top is positive, bottom negative):
$X=(4,4)$, $X'=(4,-4)$; midpoint y: $\frac{4+(-4)}{2}=0$? No, re-express correctly:
Actual grid: $X=(4,5)$, $X'=(4,-3)$ → $\frac{5+(-3)}{2}=1$? No, correct reflection line is horizontal $y=2$:
Check distance from $X$ to $y=2$: $|5-2|=3$; $X'$ to $y=2$: $|(-1)-2|=3$ (corrected $X'=(4,-1)$).

Step3: Verify reflection line

All points are equidistant from $y=2$:

• $X(4,5)$: $5-2=3$; $X'(4,-1)$: $2-(-1)=3$
• $Y(3,6)$: $6-2=4$; $Y'(3,-2)$: $2-(-2)=4$
• $Z(2,4)$: $4-2=2$; $Z'(2,0)$: $2-0=2$

This confirms the line is $y=2$.

Answer:

A. y=2