Question

Find the distance from (-2, -1, 7) and (-7, 6, 3)?Round your answer to 3 decimal places

Answer 1

To solve the exercise you can use the distance formula:

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ \text{ Where} \\ A(x_1,y_1,z_1) \\ B(x_2,y_2,z_2) \\ \text{are the coordinates of the points} \end{gathered}`

So, in this case, you have

`\begin{gathered} A(x_1,y_1,z_1)=\mleft(-2,-1,7\mright) \\ B(x_2,y_2,z_2)=\mleft(-7,6,3\mright) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ d=\sqrt[]{(-7-(-2))^2+(6-(-1))^2+(3-7)^2} \\ d=\sqrt[]{(-7+2)^2+(6+1)^2+(3-7)^2} \\ d=\sqrt[]{(-5)^2+(7)^2+(-4)^2} \\ d=\sqrt[]{25+49+16} \\ d=\sqrt[]{90} \\ d=9.487 \end{gathered}`

Therefore, the distance between the given points is approximately 9.487 units.