Question

1. what is length of fh? a. 22 b. 11 c. 26 d. 30 9. what is length of fh? a. 37 b. 7 c. 10 d. 15 10. what is length of kl? a. 100 b. 181. c. 107. d. 57 find the distance between the points to the nearest tenth 11. (-6, -7) and (-5, -2) a. 2.4 b. 14.2 c. 5.1 d. 2 12. (8,-8) and (1,4) a. 13.9 b. 4.4 c. 9.8 d. 8.2

Explanation:

Step1: Analyze problem 9

Given that $FG = 22$ and $HG=15$, to find $FH$, we use the segment - addition postulate which states that if $H$ is between $F$ and $G$, then $FG=FH + HG$.
So, $FH=FG - HG$.

Step2: Substitute values

Substitute $FG = 22$ and $HG = 15$ into the formula.
$FH=22 - 15=7$.

Step3: Analyze problem 10

Given that $JL = 144$ and $JK = 37$, to find $KL$, we use the segment - addition postulate $JL=JK + KL$.
So, $KL=JL - JK$.

Step4: Substitute values

Substitute $JL = 144$ and $JK = 37$ into the formula.
$KL=144 - 37 = 107$.

Step5: Analyze problem 11

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For points $(-6,-7)$ and $(-5,-2)$, $x_1=-6,y_1 = - 7,x_2=-5,y_2=-2$.
$d=\sqrt{(-5+6)^2+(-2 + 7)^2}=\sqrt{1^2+5^2}=\sqrt{1 + 25}=\sqrt{26}\approx5.1$.

Step6: Analyze problem 12

For points $(8,-8)$ and $(1,4)$, $x_1 = 8,y_1=-8,x_2 = 1,y_2 = 4$.
$d=\sqrt{(1 - 8)^2+(4 + 8)^2}=\sqrt{(-7)^2+12^2}=\sqrt{49+144}=\sqrt{193}\approx13.9$.

Answer:

1. B. 7
2. C. 107
3. C. 5.1
4. A. 13.9