Question

the rule $r_{y - axis} circ r_{o, 90^{circ}}(x, y)$ is applied to $\triangle abc$. which triangle shows the final image?
1
2
3
4

Explanation:

Step1: Identify ΔABC coordinates

Let’s assign coordinates from the grid:
$A=(2, -4)$, $B=(4, -4)$, $C=(4, -2)$

Step2: Apply rotation $R_{O, 90^\circ}(x,y)$

Rotation rule for 90° counterclockwise about origin: $(x,y) \to (-y,x)$

• $R_{O,90^\circ}(A) = (4, 2)$
• $R_{O,90^\circ}(B) = (4, 4)$
• $R_{O,90^\circ}(C) = (2, 4)$

Step3: Apply reflection $r_{y-axis}(x,y)$

Reflection rule over y-axis: $(x,y) \to (-x,y)$

• $r_{y-axis}(4,2) = (-4, 2)$
• $r_{y-axis}(4,4) = (-4, 4)$
• $r_{y-axis}(2,4) = (-2, 4)$

Step4: Match to grid triangles

The coordinates $(-4,2), (-4,4), (-2,4)$ correspond to Triangle 1.

Answer:

1. Triangle 1