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(x_{1}, y_{1}) and Q(x_{2}, y_{2}) on the coordinate axis. Draw PM perpendicular to OX and PR perpendicular to QN.

By Pythagoras theorem,

**Hence, the distance between the points****(x _{1}, y_{1}) and (x_{2}, y_{2})**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).

Squaring both sides

(PA)^{2} = (PB)^{2}

The coordinates of required point are .

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