Question

which figure shows △abc being reflected across the x - axis? a b c d

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected across the $x -$axis, the new point is $(x, - y)$. For a triangle $\triangle ABC$ with vertices $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$, the reflected triangle $\triangle A'B'C'$ has vertices $A'(x_1,-y_1)$, $B'(x_2,-y_2)$ and $C'(x_3,-y_3)$. This means the $x -$coordinates of the vertices remain the same and the $y -$coordinates change their signs. The reflected triangle will be directly below (or above if the original is below) the original triangle with respect to the $x -$axis.

Step2: Analyze each option

• Option A: The original $\triangle ABC$ and the reflected $\triangle A'B'C'$ have the correct relationship where the $x -$coordinates of corresponding vertices are the same and the $y -$coordinates are opposite in sign. The reflected triangle is directly below the original triangle across the $x -$axis.
• Option B: This shows a reflection across the $y -$axis as the $y -$coordinates of corresponding vertices are the same and the $x -$coordinates change their signs.
• Option C: The orientation of the reflected triangle is incorrect. It does not follow the rule of reflection across the $x -$axis.
• Option D: The orientation of the reflected triangle is wrong. It does not represent a proper reflection across the $x -$axis.

Answer:

A.