Question

Determine the scale factor for the following points: (4, 2) to (16, 8)

Answer 1

Answer:

The rule of dilation by a scale factor 4 is:

(x, y)  →  (4x, 4y)

P(4, 2)  →  (4x, 4y) = (4(4), 4(2)) = P'(16, 8)

Therefore, 4 will be the scale factor.

Step-by-step explanation:

Given the point

• (4, 2)

As the image coordinates of (4, 2) are (16, 8) after the scale factor, we need to determine what could be the scale factor.

• Let P(4, 2) is the original point, and P'(16, 8) is the image of the point P(4, 2).

It is clear that the coordinates of the image P'(16, 8) are 4 times the coordinates of the original point P(4, 2), which means the point P(4, 2) is dilated by a scale factor of 4.

Thus, the rule of dilation by a scale factor 4 is:

(x, y)  →  (4x, 4y)

P(4, 2)  →  (4x, 4y) = (4(4), 4(2)) = P'(16, 8)

Therefore, 4 will be the scale factor.