Question

What is the approximate distance between the points (-3, -4) and (-8, 1) on a coordinate grid

Answer 1

In this question is given to points, with coordinates (-3,-4) and (-8,1). It is asked to find the distance between both points. The only way to find the solution is by using the Distance Formula, which is represented by 
$d= \sqrt{( x_{2}- x_{1})^{2}+( y_{2}- y_{1})^{2}}$.

$d= \sqrt{( x_{2}- x_{1})^{2}+( y_{2}- y_{1})^{2}}$
$d= \sqrt{(-3--8)^{2}+(-4-1)^{2}}$
$d= \sqrt{(5)^{2}+(-5)^{2}$
$d= \sqrt{(25)+(25)$
$d= \sqrt{50}$
$d=7.07 units$ or $5 \sqrt{2}units$

The distance between the coordinates (-3,-4) and (-8,1) is 7.07 units or $5 \sqrt{2}units$.

Answer 2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -3 &,& -4~) % (c,d) &&(~ -8 &,& 1~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{25+25}\implies d=\sqrt{2\cdot 25}\implies d=\sqrt{2\cdot 5^2}\implies d=5\sqrt{2}$