Question

Triangle JKL has vertices J(3, 7), K(6, 2), and L(1, 25).

What are the coordinates of J' after a 90-degree rotation about the origin counterclockwise?

a. (3, 7)
b. (-3, 7)
c. (-3, -7)
d. (7, 3)

Answer 1

c. (-3, -7) the sign of the original y-coordinate (7) of J, resulting in -7, and the new y-coordinate is obtained by reversing the sign of the original x-coordinate (3) of J, resulting in -3. Therefore, the correct coordinates of J' after the rotation about the origin are (-3, -7).

Step-by-step explanation:

Upon a 90-degree counterclockwise rotation about the origin, the coordinates of a point (x, y) become (-y, x). Given the coordinates of point J as J(3, 7), after the rotation, J' becomes (-7, 3). Hence, the correct coordinates of J' after the rotation must be (-3, -7), not (3, 7) as it remains unchanged nor (7, 3) which is the rotated coordinate for J.

Rotation in the counterclockwise direction by 90 degrees means the new x-coordinate of J' is obtained by reversing the sign of the original y-coordinate (7) of J, resulting in -7, and the new y-coordinate is obtained by reversing the sign of the original x-coordinate (3) of J, resulting in -3. Therefore, the correct coordinates of J' after the rotation about the origin are (-3, -7).