Question

If point Q(6, 13) undergoes a dilation with scale factor k centered at the origin to obtain Q'(19.2, 41.6). Find k, the scale factor.

a. k = 2.4
b. k = 3.2
c. k = 4.8
d. k = 6.93

Answer 1

The scale factor k is calculated by dividing the coordinates of Q' by the corresponding coordinates of Q. For both the x-coordinate and the y-coordinate, the scale factor is found to be 3.2, which is option b. k = 3.2.

Step-by-step explanation:

To find the scale factor k for a dilation centered at the origin that changes point Q(6, 13) into point Q'(19.2, 41.6), we can compare the coordinates of Q and Q' directly. Since the dilation is centered at the origin, the coordinates of Q' should be k times those of Q.

We can calculate k for the x-coordinate by dividing the x-coordinate of Q' by that of Q:

k = 19.2 / 6

This simplifies to:

k = 3.2

We can also calculate k for the y-coordinate by dividing the y-coordinate of Q' by that of Q:

k = 41.6 / 13

Which also simplifies to:

k = 3.2

Since both calculations give the same result, the scale factor is k = 3.2.