Question

Two points A (-2, 9) and B (4, 8) lie on a line l. Find the distance between points A and B.

Answer 1

Given:

Two points:

A(-2, 9)

B (4, 8)

These points lie on a straight line.

To find:

Distance between the two points = ?

i.e. AB = ?

Solution:

We can use Distance formula to find the distance between two points on a line.

Distance formula  is given as:

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

 D is the distance between the two points whose coordinates are $(x_1, y_1)$and $(x_2, y_2)$.

Here, the points are A and B which have the following values:

$x_1 = -2\\x_2 = 4\\y_1 = 9\\y_2 = 8$

Now, using the formula:

$AB = \sqrt{(4-(-2))^2+(8-9)^2}\\\Rightarrow AB = \sqrt{(6)^2+(-1)^2}\\\Rightarrow AB = \sqrt{36+1}\\\Rightarrow AB = \sqrt{37}\ units$

So, the distance between the points A and B is $\sqrt{37}\ units$.