Question

Find the distance between the given points:

(i) A (3, -4), B (-5,6)

Answer 1

The given points are A(3, –4), B(–5, 6).
From these points, x₁ = 3, y₁ = –4, x₂ = –5, y₂ = 6.
By the distance formula,

$$\begin{gathered} \mathrm{AB}=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2} \\ =\sqrt{(-5-3{)}^2+[6-(-4){]}^2} \\ =\sqrt{(-8{)}^2+(10{)}^2} \\ =\sqrt{64+100} \\ =\sqrt{164} \\ =2\sqrt{41} \end{gathered}$$