Question

Find the distance between the points $(0,8)$ and $(6,0)$

Answer 1

The distance between the points (0, 8) and (6, 0) is
$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$=\sqrt{(6-0{)}^2+(0-8{)}^2}=\sqrt{36+64}=\sqrt{100}=10$
Aliter:
Let A and B denote the points (6, 0) and (0, 8) and let O be the origin. The point (6, 0) lies on the x-axis and the point (0, 8) lies on the y-axis. Since the angle between coordinate axes is right angle, the points A, O and B form a right triangle.
Now, OA = 6 and OB = 8. Hence, using Pythagorean Theorem
$A{B}^2=O{A}^2+O{B}^2=36+64=100$.
$\therefore AB=\sqrt{100}=10$