Chapter 7 · Question 1

State the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ .

Answer

The distance is

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

.

Use the horizontal difference and vertical difference as the legs of a right triangle.

The distance formula comes from Pythagoras theorem. If

A(x_1,y_1)

and

B(x_2,y_2)

, then horizontal distance is

|x_2-x_1|

and vertical distance is

|y_2-y_1|

. Therefore

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

.