Question

1. a point is at (3, -4) in the coordinate plane. what coordinates will the point have after a 180 degrees rotation about (3, 5)? (0, -9) (0, 1) (3, 14) (-3, 4)

Explanation:

Step1: Find the vector from the center of rotation

The center of rotation is \((3,5)\) and the point is \((3,-4)\). The vector from \((3,5)\) to \((3,-4)\) is \((3 - 3,-4 - 5)=(0,-9)\).

Step2: Apply 180 - degree rotation to the vector

A 180 - degree rotation of a vector \((x,y)\) is \((-x,-y)\). For the vector \((0,-9)\), after 180 - degree rotation, it becomes \((0,9)\).

Step3: Find the new point

To find the new point, add the rotated vector to the center of rotation \((3,5)\). So, \((3+0,5 + 9)=(3,14)\).

Answer:

\((3,14)\) (the third option)