How do you find the distance between points E(5, -2) and F(-8, 3) and the coordinates of midpoint line EF?

Question

How do you find the distance between points E(5, -2) and F(-8, 3) and the coordinates of midpoint line EF?

Answer 1

Hi.

Let coordinates of E be (x, y) and that of F be (a,b)

To find distance between two points all you have to do is to use the formula ( (x-a) ^ 2 + (y-b) ^ 2 ) ^ 1/2

To find the midpoint of EF you have to use the formula

(x+a)/2 :::::::> the answer you get is th x-coordinate of the midpoint

(y+b)/2::::::::> the answer you get is the y-coordinate of the midpoint.

I hope that I have helped you and that u will be able to do your question.

Answer 2

You find the distance by using the Pythagorean Theorem.  You start by finding the difference in rise (y-value) and run (x-value) and use those as your two sides to find the hypotenuse.  To find the midpoint, divide the two sides in half and where they connect on the hypotenuse is it.  

For example, your sides are EFx(-8 - 5 = 13) and EFy(3 - -2 = 5).  So EFx divided by two is 6 1/2.  And EFy divided by two is 2 1/2.  So take one of the points and work from that.  Point E is at (5,-2) so travel towards point F using the midpoint distances (-6.5,2.5).  That gives you point G(-1.5, 0.5) as the midpoint.