Given: The two points below
[tex]\begin{gathered} P_1:\left(-7,-9\right? \\ P_2:\left(-2,-3\right? \end{gathered}[/tex]To Determine: The distance between teh two points
Solution
The distance between two given points (Say A and B) is calculated by the formula below
[tex]\begin{gathered} A:\left(x_1,y_1\right? \\ B:\left(x_2,y_2\right? \\ D_{istance\text{ between A nd B}}\left(AB\right?=\sqrt{\left(y_2-y_1\right?^2+\left(x_2-x_1\right?^2} \end{gathered}[/tex]Substitute the given points into the formula
[tex]\begin{gathered} P_1\left(-7,-9\right),x_1=-7,y_1=-9 \\ P_1\left(-2,-3\right),x_2=-2,y_2=-3 \end{gathered}[/tex][tex]P_1P_2=\sqrt{\left(-3--9\right)^2+\left(-2--7\right)^2}[/tex][tex]\begin{gathered} P_1P_2=\sqrt{\left(-3+9\right)^2+\left(-2+7\right)^2} \\ P_1P_2=\sqrt{6^2+5^2} \\ P_1P_2=\sqrt{36+25} \\ P_1P_2=\sqrt{61} \end{gathered}[/tex][tex]\begin{gathered} P_1P_2=7.8102 \\ P_1P_2=7.81\left(nearest\text{ hundredth\rparen}\right? \end{gathered}[/tex]The formula for finding the mid point is calculated midpoint of twopoints is
[tex]M_{id\text{ point}}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right?[/tex]Substitute the given points into the formula
[tex]\begin{gathered} M_{id\text{ point of P1 and P2}}=\left(\frac{-7+-2}{2},\frac{-3+-9}{2}\right? \\ M_{id\text{ point of P1 and P2}}=\left(\frac{-7-2}{2},\frac{-3-9}{2}\right? \\ M_{id\text{ point of P1 and P2}}=\left(\frac{-9}{2},\frac{-12}{2}\right? \\ M_{id\text{ point of P1 and P2}}=\left(-4.5,-6\right? \end{gathered}[/tex]ANSWER SUMMARY
(a) The distance between the two points corrected to the nearest hundredth is 7.81
(b) The mid-point of the given points is (-4.5,-6)
