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

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

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

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.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2