Question

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

Explanation:

Step1: Recall reflection rules

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

Step2: Reflect point A across x - axis

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

Step3: Reflect point B across x - axis

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

Step4: Reflect point C across x - axis

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

Step5: Recall y - axis reflection rules

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

Step6: Reflect point A across y - axis

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

Step7: Reflect point B across y - axis

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

Step8: Reflect point C across y - axis

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

Answer:

• Reflection across the x - axis: A'(1, - 3), B'(4, - 8), C'(5, - 2)
• Reflection across the y - axis: A''(-1,3), B''(-4,8), C''(-5,2)