Question

Could you please help me with this problem of #9?

Answer 1

Given: The two points below

`\begin{gathered} P_1:\left(-7,-9\right? \\ P_2:\left(-2,-3\right? \end{gathered}`

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

`\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?=√(\left(y_2-y_1\right?^2+\left(x_2-x_1\right?^2) \end{gathered}`

Substitute the given points into the formula

`\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}`
`P_1P_2=√(\left(-3--9\right)^2+\left(-2--7\right)^2)`
`\begin{gathered} P_1P_2=√(\left(-3+9\right)^2+\left(-2+7\right)^2) \\ P_1P_2=√(6^2+5^2) \\ P_1P_2=√(36+25) \\ P_1P_2=√(61) \end{gathered}`
`\begin{gathered} P_1P_2=7.8102 \\ P_1P_2=7.81\left(nearest\text{ hundredth\rparen}\right? \end{gathered}`

The formula for finding the mid point is calculated midpoint of twopoints is

`M_{id\text{ point}}=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right?`

Substitute the given points into the formula

`\begin{gathered} M_{id\text{ point of P1 and P2}}=\left((-7+-2)/(2),(-3+-9)/(2)\right? \\ M_{id\text{ point of P1 and P2}}=\left((-7-2)/(2),(-3-9)/(2)\right? \\ M_{id\text{ point of P1 and P2}}=\left((-9)/(2),(-12)/(2)\right? \\ M_{id\text{ point of P1 and P2}}=\left(-4.5,-6\right? \end{gathered}`

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)