Question

pretest: transformations and congruence
select the correct answer from each drop-down menu.
$delta abc$ is reflected across the x-axis, then rotated $90^{\circ}$ clockwise about the origin, and finally reflected across the line $y = x$ to form $delta abc.$
the coordinates of vertex $a$ are
the coordinates of vertex $b$ are
the coordinates of vertex $c$ are

Explanation:

First, identify the original coordinates of the vertices from the graph:

• $A(1, 1)$
• $B(2, 3)$
• $C(2, 1)$

Step1: Reflect over x-axis

Rule: $(x,y) \to (x,-y)$

• $A_1(1, -1)$
• $B_1(2, -3)$
• $C_1(2, -1)$

Step2: Rotate 90° clockwise about origin

Rule: $(x,y) \to (y,-x)$

• $A_2(-1, -1)$
• $B_2(-3, -2)$
• $C_2(-1, -2)$

Step3: Reflect over $y=x$

Rule: $(x,y) \to (y,x)$

• $A'(-1, -1)$
• $B'(-2, -3)$
• $C'(-2, -1)$

Answer:

The coordinates of vertex $A'$ are $(-1, -1)$
The coordinates of vertex $B'$ are $(-2, -3)$
The coordinates of vertex $C'$ are $(-2, -1)$