The given transformations are rigid transformations, such that
the image and the preimage have the same dimensions.
Correct responses:
Given;
The images of triangle 1 are; Triangle 2, and triangle 3
Taking the image of line m as line m, we have;
Required:
The degree of the intersection of lines m and n
Solution:
Triangle 2 is the reflection of triangle 1 across line m, and
triangle 3 is the reflection of triangle 2 across line n
The distance of triangles 1 and 2 from line m are equal
The distance of triangle 2 and 3 from line n are equal.
Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is
equal to the degree of rotation of triangle 2 to triangle 3, θ₂,
we have;
θ₁ = θ₂
100° = θ₁ + θ₂ = 2·θ₁
θ₁ = θ₂ = 100° ÷ 2 = 50°
The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°
The transformation to give triangle 2 from triangle 1 is a reflection about line m.
Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.
Therefore;
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