Question

Overline BK has endpoints B(1, 4) and K(4, - 3) . Rotate overline BK clockwise 270 degrees about the origin.

Part A: Write an algebraic description of the transformation of overline BK .
Part B: What are the endpoints of the new line segment ?

Answer 1

To rotate the line segment BK clockwise 270 degrees about the origin, use the rotation formula with the given endpoints B(1, 4) and K(4, -3). The new endpoints are B'(4, -1) and K'(4, -1).

Step-by-step explanation:

To rotate a line segment clockwise 270 degrees about the origin, we can use the rotation formula:

x' = x cos(theta) - y sin(theta)

y' = x sin(theta) + y cos(theta)

In this case, the line segment BK has endpoints B(1, 4) and K(4, -3).

Substituting these values into the rotation formula with theta = 270 degrees:

x' = 1 cos(270) - 4 sin(270) = 4

y' = 1 sin(270) + 4 cos(270) = -1

Hence, the new endpoints of the line segment are B'(4, -1) and K'(4, -1).