Question

Line segmentAB has vertices A(−3, 4) and B(1, −2) . A dilation, centered at the origin, is applied to AB⎯⎯⎯⎯⎯ . The image has vertices A′(−1, 43) and B′(13, −23) .
What is the scale factor of the dilation?

16

13

3

6

Answer 1

Answer:

The scale factor is

$\frac{1}{3}$

Step-by-step explanation:

Line segmentAB has vertices A(−3, 4) and B(1, −2) .

A dilation, centered at the origin, is applied to AB. The image has vertices

A'(-1,4/3) and B′(1/3, −2/3) .

We know the rule for dilation by scale factor of k, is

$(x,y)\to(kx,ky)$

This means that;

$A(-3,4)\to A'(-3k,4k)$

But we know, A' has coordinates (-1,4/3)

This means that

$- 3k = - 1$

$k = \frac{1}{3}$

We could also compare:

4k=4/3

Which gives

k=⅓

Answer 2

Answer:

1/3

Step-by-step explanation: