## DISTANCE FORMULA

The perpendicular distance of a point from the y-axis is called x-coordinate and the perpendicular distance of a point from the x-axis is called y-coordinate. The coordinates of a point on the x-axis is in form of (x, 0) and the point on the y-axis is in the form of (0, y). The x – coordinate is called abscissa and the y – coordinate is called ordinate.

The distance formula help to find out the length of the straight line between any two points. The distance formula is derived using a Pythagoras’s Theorem.

Consider two points P(x1, y1) and Q(x2, y2) on the coordinate axis. Draw PM perpendicular to OX and PR perpendicular to QN.

By Pythagoras theorem,

Hence, the distance between the points(x1, y1) and (x2, y2)is written as follows:

Question 1:

Find the distance between two points A(2, 4) and B(4, 5).

Solution 1:

Use the distance formula

Let , substitute the values as follows:

Therefore, the distance between two points is 2.24 units.

Question 2:

Find the distance between two points P(5, 3) and Q(9, 10).

Solution 2:

The distance between two points is determined as follows:

Use the distance formula

Let , substitute the values as follows:

Therefore, the distance between two points is 8. 06 units.

Question 3:

Find a point on x – axis which is equidistant from the points (3, 2) and (–1, 3).

Solution 3:

Let a point P(x, 0) lie on x – axis which is equidistant from the points A(3, 2) and B(–1, 3).

PA = PB

Squaring both sides

(PA)2 = (PB)2

The coordinates of required point are .