Question

Line segment AB has vertices A(-3, 4) and B(1, -2). A dilation centered at the orgin is applied to AB. The image has vertices A(-1, 4/3) and B(1/3, -2/3). What is tjr scale factor of the dilation?
1. 1/6
2. 1/3
3. 3
4. 6​

Answer 1

Answer:

option 2

Step-by-step explanation:

consider the coordinates A (- 3, 4 ) and A' (- 1, $\frac{4}{3}$ )

since the dilatation is centred at the origin, then corresponding coordinates are multiples/ divisors of each other, then image to original gives scale factor.

scale factor = $\frac{A'}{A}$ = $\frac{-1}{-3}$ = $\frac{1}{3}$ and $\frac{\frac{4}{3} }{4}$ = $\frac{1}{3}$

similarly B (1, - 2 ) and B' ($\frac{1}{3}$, - $\frac{2}{3}$ )

$\frac{\frac{1}{3} }{1}$ = $\frac{1}{3}$ and $\frac{-\frac{2}{3} }{-2}$ = $\frac{1}{3}$