Question

x’ y’ has endpoints located at x’ (0,8) and y’(0,2). it was dilated at the scale factor of 2 from center (0,2). which statement describes the pre-image?

Answer 1

The statement for the line segment XY and its endpoint coordinates is: XY has endpoints located at X (0, 5) and Y (0, 2).

What statement does represent the pre-image of a line segment?

Herein we find the coordinates of the endpoints of the image of line segment XY, which is the result of a rigid transformation known as dilation, whose definition is shown below:

X'(x, y) = O(x, y) + k · [X(x, y) - O(x, y)]

Y'(x, y) = O(x, y) + k · [Y(x, y) - O(x, y)]

If we know that X'(x, y) = (0, 8), Y'(x, y) = (0, 2), O(x, y) = (0, 2) and k = 2, then the coordinates of the pre-image are:

(0, 8) = (0, 2) + 2 · [X(x, y) - (0, 2)]

(0, 6) = 2 · [X(x, y) - (0, 2)]

(0, 3) = X(x, y) - (0, 2)

X(x, y) = (0, 5)

(0, 2) = (0, 2) + 2 · [Y(x, y) - (0, 2)]

(0, 0) = 2 · [Y(x, y) - (0, 2)]

(0, 0) = Y(x, y) - (0, 2)

Y(x, y) = (0, 2)

The statement of the line segment that is the pre-image is shown below: XY has endpoints located at X (0, 5) and Y (0, 2).