Answer:
The scale factor is
[tex] \frac{1}{3} [/tex]
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
[tex](x,y)\to(kx,ky)[/tex]
This means that;
[tex]A(-3,4)\to A'(-3k,4k)[/tex]
But we know, A' has coordinates (-1,4/3)
This means that
[tex] - 3k = - 1[/tex]
[tex]k = \frac{1}{3} [/tex]
We could also compare:
4k=4/3
Which gives
k=⅓
