Question

part 2 - find the distance between the two points. use the distance formula. $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

1. $p(3,4)$ and $q(7, - 2)$
2. $m(-4,9)$ and $n(-5,3)$

part 4 - find the midpoint of the given points. $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

1. find the midpoint of $a(6, - 2)$ and $b(-2, - 8)$
2. find the midpoint of $c(-1,5)$ and $d(-6, - 8)$

part 5 - find the indicated segment. (hint: you should draw and label a picture)

1. suppose $m$ is the midpoint of $overline{fg}$, $fm = 3x - 4$, $mg = 5x - 26$. find $fg$.

Explanation:

8)

Step1: Identify coordinates

Let $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(7, - 2)$.

Step2: Apply distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(7 - 3)^2+(-2 - 4)^2}$
$=\sqrt{4^2+(-6)^2}=\sqrt{16 + 36}=\sqrt{52}=2\sqrt{13}$

9)

Step1: Identify coordinates

Let $(x_1,y_1)=(-4,9)$ and $(x_2,y_2)=(-5,3)$.

Step2: Apply distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(-5+4)^2+(3 - 9)^2}$
$=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}$

10)

Step1: Identify coordinates

Let $(x_1,y_1)=(6,-2)$ and $(x_2,y_2)=(-2,-8)$.

Step2: Apply mid - point formula

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1 + y_2}{2})=(\frac{6+( - 2)}{2},\frac{-2+( - 8)}{2})$
$=(\frac{4}{2},\frac{-10}{2})=(2,-5)$

11)

Answer:

1. $2\sqrt{13}$
2. $\sqrt{37}$
3. $(2,-5)$
4. $(-\frac{7}{2},-\frac{3}{2})$
5. $58$