Triangle p is reflected in the line y = -x to give triangle q. Triangle q is reflected in the line x= -1 to give triangle r. describe fully the single transformation that maps triangle r to triangle p

The single transformation that maps triangle r to triangle p is +90° (countrer clockwise) rotation about the point (-1, 0)

Explanation:

The coordinates change from reflection across y = -x is given as follows;

p = (x, y) becomes q = (-y, -x)

The reflection across the line x = -1 = reflection across the y-axis at x = -1

Reflection across the y-axis gives;

(x, y) → (-x, y)

The reflection across the line x = -1  gives;

(x, y) → (-x - 1, y)

Therefore;

q = (-y, -x) becomes r = (y -1, -x)

Hence the total transformation is presented as follows;

p = (x, y) becomes r = (y -1, -x)

y = -1 - x

Rotation of a coordinate about a point

x' = x×cosθ - y×sinθ

y' = y×cosθ + x×sinθ

Whereby we rotate -90° about the point (-1, 0), we have;

x = x'×cos(-90) - y'×sin(-90) -1 = y' - 1

y = y'×cos(-90) + x'×sin(-90) + 0 = -x'

Therefore, the single transformation that maps triangle p to triangle r is -90° rotation about the point (-1, 0)

Conversely, the single transformation that maps triangle r to triangle p is 90° rotation about the point (-1, 0).

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