Question

Angle ABC is formed by segments AB and BC on the following coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment AB is shown with A as ordered pair 1, negative 1 and B as ordered pair 5, negative 4. Another line segment BC is shown with C as ordered pair 1, negative 4. Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle A'B'C'. Which statement shows the measure of angle A'B'C'? A) m∠ A'B'C' = 90 degrees B) m∠ A'B'C' = m∠ABC C) m∠ A'B'C' = 180 degrees D) m∠ A'B'C' = 2 ⋅ m∠ABC

Answer 1

B) m∠ A'B'C' = m∠ABC

Explanation:

A rotation does not change angle measure or side length. It preserves congruence.

This means that the image angle, A'B'C', will be congruent to the pre-image angle, ABC.

Answer 2

Option: B is the correct answer.

B) m∠ A'B'C' = m∠ABC

Explanation:

We are given coordinates of Point A,B and C as:

A(1,-1) , B(5,-4) and C(1,-4)

Since, on rotating the points 90 degree counterclockwise about the origin the rule that holds for this transformation is:

(x,y) → (-y,x)

Hence,

A(1,-1) → A'(1,-1)

B(5,-4) → B'(4,-5)

C(1,-4) → C'(4,-1)

As we know that the rotation is a rigid transformation that is the shape and size of the figure is preserved.

Also, the angle measure remains the same.

Hence, m∠ABC=m∠A'B'C'