Question

find the distance between the given points. If the answer is not exact, use a calculator and give an approximation to the nearest tenth.(-7,4), (5,8)

Answer 1

The given points are,

`\begin{gathered} (x_1,y_1)=\mleft(-7,4\mright) \\ (x_2,y_2)=\mleft(5,8\mright)​ \end{gathered}`

The distnace between the two point formula is,

`D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}^2`

subsitute the points in the formula,

`\begin{gathered} D=\sqrt[]{(5-(-7))^2+(8-4)^2} \\ =\sqrt[]{(5+7)+(8-4)^2} \\ =\sqrt[]{(12)^2+(4)^2} \\ =\sqrt[]{144+16} \\ =\sqrt[]{160} \\ =\sqrt[]{16*10} \\ =\sqrt[]{4*4*10} \\ =4\sqrt[]{10} \\ =4*3.162 \\ =12.64 \\ \end{gathered}`

the answer is 12.6.ok