Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by? Answer choices:
A. 1/2
B. 2
C. 3
D.4

Given:

Endpoint of segment AB are A(0,2), B(2,3).

Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).

To find:

The scale factor of dilation.

Solution:

If a figure is dilated about the origin with factor k, then

Using this rule, we get

So, the image of A is A'(0,2k).

It is given that image of A is A'(0,4). So,

On comparing the y-coordinates from both sides, we get

Therefore, the scale factor is 2 and the correct option is B.

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