Question

What is the approximate distance between the points (-3, -4) and (-8, 1) on a coordinate grid? A. 11.40 units B. 7.07 units C. 3.16 units D. 12.08 units

Answer 1

The formula of the distance between two points:

$A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

We have:

$A(-3;-4);\ B(-8;\ 1)$

substitute:

$|AB|=\sqrt{(-8-(-3))^2+(1-(-4))^2}=\sqrt{(-8+3)^2+(1+4)^2}\\\\=\sqrt{(-5)^2+5^2}=\sqrt{25+25}=\sqrt{25\cdot2}=\sqrt{25}\cdot\sqrt2\\\\=\boxed{5\sqrt2\approx7.07}$

Answer: B. 7.07