Question

What is the approximate distance between the points (-2, 3, -5) and (2, -7, 4)?

A. 14

B. 23

C. 11

D. 17

Answer 1

`\text{The formula of a distance between two points}\\\\A(x_A;\ y_A;\ z_A);\ B(x_B;\ y_B;\ z_B)\\\\|AB|=√((x_B-x_A)^2+(y_B-y_A)^2+(z_B-z_A)^2)\\\\\text{We have}\ A(-2;\ 3;\ -5);\ B(2;\ -7;\ 4)\\\\\text{substitute}\\\\|AB|=√((2-(-2))^2+(-7-3)^2+(4-(-5))^2)\\\\=√(4^2+(-10)^2+9^2)=√(16+100+81)=√(197)\approx14\\\\\text{Answer:}\ A.\ 14`