Question

A vertex of a rectangle on the coordinate plane is (8, 12). The rectangle is dilated with the center of dilation at the origin. The new coordinate after the dilation is (2, 3). What is the scale factor?

a) 4

b) 1/2

c) 1/4

d) 2

Answer 1

The scale factor of the rectangle is 1/4.

Step-by-step explanation:

The scale factor can be calculated by finding the ratio of the corresponding sides of the original rectangle and the dilated rectangle.

The original rectangle has a vertex at (8, 12) and after dilation, the new coordinate is (2, 3).

Let's calculate the scale factor:

The horizontal scale factor is calculated as the change in x-coordinate of the vertices:

(new x-coordinate - old x-coordinate) / old x-coordinate = (2 - 8) / 8 = -6/8 = -3/4

The vertical scale factor is calculated as the change in y-coordinate of the vertices:

(new y-coordinate - old y-coordinate) / old y-coordinate = (3 - 12) / 12 = -9/12 = -3/4

Since both the horizontal and vertical scale factors are the same, we can conclude that the scale factor is -3/4, which can be simplified to 1/4.