Distance between Two points (Two Dimensions)

Distance between Two points (Two Dimensions) :

Let P(x_1,y_1) and Q(x_2,y_2) are two points in a plane,distance between them is d.

Now we have to find the distance d, draw two perpendiculars on x axes from P and Q points, which are PM and QN, now draw a perpendicular PR from point P on QN.

distance formula

According to the above figure:

OM =x_1 ; PM = y_1

ON = x_2 ; QN = y_2

So PR = MN = ON – OM = x_2 -x_1

And QR = QN – RN  = QN – PM = y_2 -y_1

Now In right triangle PRQ :

PQ = \sqrt{PR^2 + QR^2}

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

Or d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}  ….( distance formula)

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