Question

**#4.) rahma and zion live at the locations below. who lives closer to the school? mathematically justify your answer.
*#5.) $overline{ab}$ with endpoints $a(12, - 3)$ and $b(-2, - 3)$ and $overline{cd}$ with endpoints $c(0,4)$ and $d(-9,-8)$. determine and state which segment is longer.
a.) $ab$
b.) $cd$
c.) theyre the same length
d.) $mn$
**#6.) ms. nolan loves the beach but her biggest fear is getting attacked by a shark - no dark waters for her! whats your biggest fear? why?

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $AB$

For $A(12,-3)$ and $B(-2,-3)$, $x_1 = 12,y_1=-3,x_2=-2,y_2 = - 3$. Since $y_1=y_2$, $AB=\vert12-(-2)\vert=\vert12 + 2\vert=14$.

Step3: Calculate length of $CD$

For $C(0,4)$ and $D(-9,-8)$, $x_1 = 0,y_1 = 4,x_2=-9,y_2=-8$. Then $CD=\sqrt{(-9 - 0)^2+(-8 - 4)^2}=\sqrt{(-9)^2+(-12)^2}=\sqrt{81 + 144}=\sqrt{225}=15$.

Answer:

b. $CD$