Question

which statement correctly describes the diagram?

triangle b is a reflection of triangle a across the x - axis. triangle c is a reflection of triangle a across the line y = x.
triangle b is a reflection of triangle a across the x - axis. triangle c is not a reflection of triangle a.
triangle b is a reflection of triangle a across the y - axis. triangle c is not a reflection of triangle a.
triangle b is a reflection of triangle a across the y - axis. triangle c is a reflection of triangle a across the line y = x.

Explanation:

1. Check reflection of A to B: The x-axis reflection rule is $(x,y)\to(x,-y)$. Triangle A has vertices (2,2), (4,2), (4,6). Applying the rule gives (2,-2), (4,-2), (4,-6), which matches Triangle B. So B is a reflection of A across the x-axis.
2. Check reflection of A to C: The line $y=x$ reflection rule is $(x,y)\to(y,x)$. Applying this to A's vertices gives (2,2), (2,4), (6,4). These do not match Triangle C's vertices (-5,3), (-5,6), (-2,6). So C is not a reflection of A across $y=x$, nor is it a valid reflection over any axis relative to A.
3. Match this to the correct option.

Answer:

Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.