Question

△XYZ with vertices X(1, 1), Y(3, 5), and Z(5, 1) will be rotated 180° about the origin. What will be the coordinates of Y ?

A) Y(3, 5)
B) Y(-3, -5)
C) Y(-5, -3)
D) Y(5, 3)

Answer 1

To rotate the point Y(3, 5) 180° about the origin, we can use the rotation formula. Applying the formula, the new coordinates of Y are (-3, -5).

Step-by-step explanation:

To rotate a point (x, y) 180° about the origin in a coordinate system, we can use the rotation formula:

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

Let's apply this formula to find the new coordinates of Y(3, 5):

x' = 3 * cos(180°) - 5 * sin(180°)
y' = 3 * sin(180°) + 5 * cos(180°)

After evaluating the equations, we get: Y(-3, -5). Therefore, the correct answer is option B) Y(-3, -5).