Question

what are the coordinates of point T’, the image of point T(-2,5) after a rotation of 180 about the origin

Answer 1

The coordinates of point T' after a 180-degree rotation around the origin are (2, -5).

Step-by-step explanation:

The coordinates of point T', the image of point T(-2,5) after a rotation of 180 degrees about the origin, are found using the rotation transformation equations for a point (x, y):

• x' = x cos(180°) - y sin(180°)
• y' = x sin(180°) + y cos(180°)

Since cos(180°) = -1 and sin(180°) = 0, the transformed coordinates (x', y') are

• x' = (-2) * (-1) - 5 * 0 = 2
• y' = (-2) * 0 + 5 * (-1) = -5

Therefore, the coordinates of T' are (2, -5).

Answer 2

T'(2, - 5 )

Step-by-step explanation:

Under a rotation about the origin of 180°

a point (x, y ) → (- x, - y ), thus

T(- 2, 5 ) → T'(2, - 5 )