Question

The point P(-2,-5) is rotated 90° about the origin, and then the image is reflected across the line x-3. What are the coordinates of the final image pu?

a) (5,-2)
b) (2,5)
c) (-5,2)
d) (-2,5)

Answer 1

After rotating the point P(-2,-5) 90° around the origin, we obtain P'(5,2). Reflecting P' across the line x-3, we get the final coordinates of the reflected point as (1,2).

Step-by-step explanation:

First, let us handle the rotation of point P(-2,-5). When we rotate a point 90° around the origin in the coordinate system, the x-coordinate becomes the negative of the y-coordinate, and the y-coordinate becomes the x-coordinate. Therefore, after a 90° rotation, the new coordinates of P will be P'(5,2).

Next, we reflect point P' across the line x-3. To perform this reflection, we need to find a point on the other side of the line x-3 that is equidistant to P' as P' is from the line. Since P' has an x-coordinate of 5, and the line of reflection is x-3, we go 2 units to the right of the line (because 5 - 3 = 2) to find the reflection point. Hence, we move 2 units to the left of the line from P' to find its reflection, which results in a new x-coordinate of 1 (3 - 2 = 1). The y-coordinate remains the same during this reflection. Therefore, the final coordinates of the reflection of point P' across the line x-3 will be (1,2).