Question

1. substitute in the values to be able to determine the mid - point of segment pq. p(-1,3) and q(5,-7) (2,-2) 2. substitute in the values to be able to determine the length of segment ab. a(-8,9) and b(3,-6) d = \sqrt{(x_2 - x_1)+(y_2 - y_1)} formula d = \sqrt{(3-(-8))+( - 6 - 9)} stop 3. substitute in the values to be able to determine the length of segment ab. a(5,7) and b(-2,-8) d = \sqrt{( )+( )} formula d = \sqrt{( )+( )} stop 4. determine the length of segment st. complete this example. s(4,6) and t(-3,9) d = \sqrt{(x_2 - x_1)+(y_2 - y_1)} formula

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: For points $A(3,7)$ and $B(- 2,-8)$

Substitute $x_1 = 3,y_1 = 7,x_2=-2,y_2 = - 8$ into the formula.
$d=\sqrt{(-2 - 3)^2+(-8 - 7)^2}=\sqrt{(-5)^2+(-15)^2}=\sqrt{25 + 225}=\sqrt{250}=5\sqrt{10}$.

Step3: For points $S(4,6)$ and $T(-3,9)$

Substitute $x_1 = 4,y_1 = 6,x_2=-3,y_2 = 9$ into the formula.
$d=\sqrt{(-3 - 4)^2+(9 - 6)^2}=\sqrt{(-7)^2+3^2}=\sqrt{49+9}=\sqrt{58}$.

Answer:

For points $A(3,7)$ and $B(-2,-8)$, the distance $d = 5\sqrt{10}$.
For points $S(4,6)$ and $T(-3,9)$, the distance $d=\sqrt{58}$.