Question

Help with this question ASAP!!!

Answer 1

Answer:

The bottom choice.

Step-by-step explanation:

To get from H to F, you need to show the ratio as 6:4 which is 2:3 or 2/3 which means that A and C  are are incorrect.

To get from - 10 to D, you need to take 2/3 of G or 2/3 of - 10

2/3 * - 10 = -20/3

That means that D = 0,-20/3

The answer is the last choice.

Answer 2

Answer:

$\large\boxed{D\left(0,\ -\dfrac{20}{3}\right),\ \dfrac{2}{3}}$

Step-by-step explanation:

$\triangle FOD\sim\triangle HOG,\ \text{therefore the sides are in proportion:}\\\\\dfrac{OF}{OD}=\dfrac{OH}{OG}\\\\\text{We have}\\\\OF=4,\ \ OH=6,\ OG=10\\\\\text{Substitute:}\\\\\dfrac{4}{OD}=\dfrac{6}{10}\qquad\text{cross multiply}\\\\6OD=(4)(10)\\\\6OD=40\qquad\text{divide both sides by 6}\\\\OD=\dfrac{40}{6}\\\\OD=\dfrac{20}{3}\\\\\text{Therefore}\ D\left(0,\ -\dfrac{20}{3}\right).\\\\\text{The scale factor:}\ \dfrac{OF}{OH}=\dfrac{4}{6}=\dfrac{2}{3}$