Question

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

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -3 &,& -4~) % (c,d) &&(~ -8 &,& 1~) \end{array} \\\\\\ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{(-5)^2+5^2}\implies d=\sqrt{50}\implies d=\sqrt{25\cdot 2}\implies d=\sqrt{5^2\cdot 2} \\\\\\ d=5\sqrt{2}$

Answer 2

Answer: 5.83 units

Step-by-step explanation:

The distance between points A(a,b) and B(c,d) is given by :-

$\text{Distance}=\sqrt{(d-b)^2+(c-a)^2}$

Given points :  (-3,-4) and (-8,1)

Now, the distance between the two points  (-3,-4) and (-8,1) is given by :-

$\text{Distance}=\sqrt{(1-4)^2+(-8-(-3))^2}\\\\\Rightarrow\ \text{Distance}=\sqrt{(-3)^2+(-8+3)^2}\\\\\Rightarrow\ \text{Distance}=\sqrt{9+(-5)^2}=\sqrt{9+25}\\\\\Rightarrow\ \text{Distance}=\sqrt{34}=5.83095189485\approx5.83\text{ units}$

Hence, the approximate distance between the points (-3,-4) and (-8,1) on a coordinate grid is 5.83 units.