Find the distance between the points (-2, 3) and (4, -5)

Question

Find the distance between the points (-2, 3) and (4, -5)

Answer 1

Two ways to do this, one using geometry and the other algebraic formula.

 

Way One( geometry):

 

       If you make a plot of the points (-2,3) and (4, -5) and then draw two  a line through the former parallel to the y-axis and a line through the latter parallel to the x-axis, you will form a right triangle.  It's base will be 6 units long and its altitude will be 8 units long.  This makes it a similar triangle to a 3,4,5:  it is a 2x3, 2x4 and 2x5 = 10.  So 10 is your answer.

 

Way Two (Formula)

 

        The formula is d = sqr rt [(3-(-5))² + (-2-4)²]=sqrt(64 + 36) = 10

 

So, you get the same answer as you must and can you not see that this is the Pythgorean theorem with the sum of the squares equal to the square of the hypotenuse?