Question

Find the distance between the two points.(-3, -1) (-1,-5) We have to use a^2 + b^2 = c^2

Answer 1

The formula between the distance (c) is,

$c=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Where,

$\begin{gathered} a=(x_2-x_1) \\ b=(y_2-y_1) \end{gathered}$

Given

$\begin{gathered} (x_1,y_1)=(-3,-1) \\ (x_2,y_2)=(-1,-5) \end{gathered}$

Therefore,

$c=\sqrt{(-1--3)^2+(-5--1)^2}$

Simplify

$\begin{gathered} c=\sqrt{(-1+3)^2+(-5+1)^2}=\sqrt{2^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=\sqrt{4\times5} \\ c=\sqrt{4}\times\sqrt{5}=2\times\sqrt{5}=2\sqrt{5}=\:4.47213\approx4.5 \end{gathered}$

Hence, the answer is

$c=4.5$