Question

1. a triangle with vertices p(1, 4), q(3, -2), r(-2, 1) is reflected across the line x = 0, then across the line y = 0.

a. give the coordinates of p\, q\, and r\. (3 points)
p\: ( ) q\: ( ) r\: ( )
b. which single rigid transformation does this composition represent? (1 point)

Explanation:

Step1: Recall reflection rule for line x = 0

Reflection across the line x = 0 (y - axis) has the rule (x,y)→(-x,y).

Step2: Apply rule to point P(1,4)

For point P(1,4), when reflected across x = 0, the x - coordinate changes sign. So P'(-1,4). Then reflecting across y = 0 (x - axis) with rule (x,y)→(x, - y), we get P''(-1,-4).

Step3: Apply rule to point Q(3,-2)

For point Q(3,-2), reflecting across x = 0 gives Q'(-3,-2). Then reflecting across y = 0 gives Q''(-3,2).

Step4: Apply rule to point R(-2,1)

For point R(-2,1), reflecting across x = 0 gives R'(2,1). Then reflecting across y = 0 gives R''(2,-1).

For part b, a reflection across the x - axis followed by a reflection across the y - axis is equivalent to a 180 - degree rotation about the origin. A 180 - degree rotation about the origin has the rule (x,y)→(-x,-y), which is a single rigid - transformation.

Answer:

a. P''(-1,-4), Q''(-3,2), R''(2,-1)
b. A 180 - degree rotation about the origin.