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 ????

8 Answers

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  • 1 decade ago
    Best Answer

    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
    1 decade ago

    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
    1 decade ago

    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].

  • 1 decade ago

    Just cite the Pythagorean Theorem

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  • Philo
    Lv 7
    1 decade ago

    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.

  • 1 decade ago

    insert numbers for the variables- try 1 number for x and 1 number y.

  • Anonymous
    5 years ago

    32d3ff

  • 1 decade ago

    Please use Pythegorian theorm.

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