Question

Angle QRS has a measure of 35∘. Triangle QRS is rotated 90∘ clockwise about point R to create angle Q'R'S'

What is the measure of angle Q'R'S'?

Answer 1

Answer:

The measure of angle Q'R'S' is 35°

Step-by-step explanation:

The given parameters are;

The measure of angle QRS = 35°

The transformation applied to triangle QRS = 90° clockwise rotation

For a 90° clockwise rotation, we have;

Coordinate of the preimage (x, y), coordinate of the image after rotation (y, -x)

Given that the distance, d, between points is given by √((x₂ - x₁)² + (y₂ - y₁)²), we have that the distance between points of the image will be given as follows;

d' =√((y₂ - y₁)² + ((-x₂) - (-x₁))²) = √((y₂ - y₁)² + (x₁ - x₂)²)

Whereby we have √((y₂ - y₁)² + (x₁ - x₂)²) = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, d = d' and the length of the sides and measures of the angles in ∠QRS and ∠Q'R'S' will be equal and ∠Q'R'S' = ∠QRS = 35°.

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