Find the distance between the following points: (-2,4),(3,2)

Question

Find the distance between the following points: (-2,4),(3,2)

Answer 1

Form a right triangle as follows:

 

connect the two points you mention: this segment will be the hypotenuse

 

Now, pretend that the two points are opposite corners of a rectangle where the sides of the rectangle are strictly along the x and y grid lines.  Where the sides of this rectangle meet is the right vertex of the triangle (the two sides are the two legs of the triangle).

 

Why are we doing this?  Well, in this right triangle you have constructed, what are the lengths of the legs of the triangle (this is why it was convenient to draw them along grid lines)?

 

Now, if we know two legs of a right triangle, how can we solve for the hypotenuse?

 

If you get that, here is a general exercise:  given points (x1,y1) and (x2,y2), derive a formula to represent the distance between them.

Answer 2

To find the distance, use the the Pythagorean Theorem:

 

distance² = (change in x)² + (change in y)²

 

Where the "change in x" is the difference between the x-coordinates of the two points and the "change in y" is the difference between the y-coordinates of the two points.  These two form the legs of the right triangle and the distance between the two points is the hypotenuse.  Plugging in the x and y values of the two points:

 

d² = (3 - (-2))² + (2 - 4)²

 

d² = 5² + (-2)²

 

Can you finish it from here?