Question

Find a so the distance between (x, -7) and (-4, -2) is √89x =

Answer 1

Step-by-step explanation:

The coordinates are given below as

`\begin{gathered} (x,-7),(-4,-2) \\ d=√(89) \end{gathered}`

Concept:

The distance formula to be used is given below as

`d^2=(x_2-x_1)^2+(y_2-y_1)^2`

By substituing the values, we will have

`\begin{gathered} d^(2)=(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2) \\ (√(89))^2=(-4-x)^2+(-2-(-7)^2 \\ 89=(-4-x)^2+(-2+7)^2 \\ 89=(-4-x)^2+(5^2) \\ 89=(-4-x)^2+25 \\ (-4-x)^2=89-25 \\ (-4-x)^2=64 \end{gathered}`

Square root both sides, we will have

`\begin{gathered} (-4-x)^2=64 \\ -4-x=√(64) \\ -4-x=\pm8 \\ x=-4\pm8 \\ x=-4+8,x=-4-8 \\ x=4,x=-12 \end{gathered}`

Hence,

The final answers are

`x=-12,4`