Question

Help with this question ASAP!!!

Answer 1

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

Explanation:

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

Answer 2

The bottom choice.

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.