Question

given a triangle with the vertices a(1, 3), b(4, 8), and c(5, 2). determine the vertices of each described transformation.
① a reflection across the x - axis
② a reflection across the y - axis

Explanation:

Step1: Recall reflection rule across x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$.

Step2: Apply rule to point A(1,3)

For point A(1,3), after reflection across the x - axis, $A'=(1, - 3)$.

Step3: Apply rule to point B(4,8)

For point B(4,8), after reflection across the x - axis, $B'=(4,-8)$.

Step4: Apply rule to point C(5,2)

For point C(5,2), after reflection across the x - axis, $C'=(5,-2)$.

Step5: Recall reflection rule across y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(-x,y)$.

Step6: Apply rule to point A(1,3)

For point A(1,3), after reflection across the y - axis, $A'=(-1,3)$.

Step7: Apply rule to point B(4,8)

For point B(4,8), after reflection across the y - axis, $B'=(-4,8)$.

Step8: Apply rule to point C(5,2)

For point C(5,2), after reflection across the y - axis, $C'=(-5,2)$.

Answer:

a. $A'(1,-3)$, $B'(4,-8)$, $C'(5,-2)$
b. $A'(-1,3)$, $B'(-4,8)$, $C'(-5,2)$