# How to prove the distance formula of Co-ordinate geometry i.e Pq = √(x2 – x1)2 + (y2 – y1 )2?

Pq = √(x2 – x1)2 + (y2 – y1 )2 is the formula for distance in co-ordinate geometry.How can i prove this ????

Relevance

To test the answer for yourself, you can substitute in numbers - however, this is not a proof.

The proof is simple - this is an application of Pythagoras' theorem, that a² + b² = c². Here, a is the x difference (i.e. x2 - x1), b is the y difference (i.e. y2 - y1) and c is the actual distance.

For a proof of Pythagoras' Theorem, see http://en.wikipedia.org/wiki/Pythagorean_theorem.

• Susan
Lv 4

This would be difficult to do on this site, but let me get you started.

first: plot 2 points (x1,y1) and (x2,y2) on an x-y axis (doesn't matter where)

then: connect those 2 points. This segment will be a hypotenuse of a right triangle.

now: draw the 2 legs of the right triangle with the above as its hypotenuse.

finally: plug these values into the pythagorean theorem c^2=a^2+b^2

• Retsum
Lv 6

Sketch an x and y-axis. Mark two points P(x[1], y[1]) ans Q(x[2], y[2]). Draw a line joining PQ. Now construct a right angled triangle with PQ as the hypotenuse. Apply pythagoras to the triangle noting that one side is (y[2] - y[1]) and the other is x[2] - x[1].

Just cite the Pythagorean Theorem

• Philo
Lv 7

the line segment connecting the points + a vertical from the one with the highest y coordinate and a horizontal from the one with the smallest x coordinate give you a right triangle. those differences of coordinates give you the length of the vertical and horizontal sides. your proof is just the pythagorean theorem.