Do you know how to find **distance between two points** in coordinate geometry? This is the first formula we are going to learn in coordinate geometry.

Hope that you know how to represent a point in coordinate system. Suppose if we are given any two points and we are asked to find distance between them, then how to find it. Now let us learn **formula** for finding **distance between two points**.

**Formula for finding distance between two points:**

Consider a coordinate system. Now let us take two points in the coordinate system as shown in figure. Let the two points coordinates be P (x_{1} , y_{1}) and Q (x_{2}, y_{2}). Now PQ we will get a line segment PQ. Now let us start deriving the **formula** for **distance between two points** i.e. P and Q. for this we have to do a small construction.

Construction:

First draw a perpendicular line from point P to x-axis and name the intersecting point as C.

Similarly from point Q draw a perpendicular line to x-axis and name the intersecting point as D.

Now through the point P, draw a perpendicular line to the line QD and name the intersecting point as R.

From the diagram,

OD = x_{2} units

OC = x_{1} units

CD = OD – OC = x_{2} – x_{1 } units

Therefore, PR = CD = x_{2} – x_{1 } units

QD = y_{2} units

RD = y_{1} units

QR = QD – RD= y_{2} – y_{1} units.

The obtained PQR is a right triangle. So that we can make use of Pythagoras theorem.

According to Pythagoras theorem, we can say that

(Hyp)^{2} = (side1)^{2} + (side2)^{2}

(PQ)^{2} = (PR)^{2} + (QR)^{2}

(PQ)^{2} = (x_{2} – x_{1 })^{2} + (y_{2} – y_{1})^{2}

So the **distance between the points** P and Q is given by the formula

I explained only the basic formula but in this still we have so many cases, that we will see later.

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