Question

A vertex of a rectangle on the coordinate plane is (3,4). A dilation is applied, and the new point is (12,16). What is the scale factor of the dilation from the old to the new coordinate?

a) 2
b) 4
c) 3
d) 1/2

Answer 1

The scale factor for the dilation from the point (3,4) to (12,16) is 4, this allows us to calculate actual dimensions from scale dimensions using a simple proportion.

Step-by-step explanation:

The question asks to find the scale factor of a dilation that transforms the point (3,4) to (12,16) in a coordinate plane. To find the scale factor, we compare the coordinates of the new point to the original point. The x-coordinate goes from 3 to 12, and the y-coordinate goes from 4 to 16. Dividing the new coordinates by the original coordinates (12÷3 and 16÷4), we find both result in a scale factor of 4. Therefore, the scale factor from the old to the new coordinate is 4.

Using this information, we can solve a problem involving scale. When the scale dimension is given, such as 4 in this hypothetical case, we can set up a proportion like 1:2=4:x to calculate the actual dimension x.