SOLUTION: will you please explain to me how to do this using an equation. i am so lost. It says, find the distance and the midpoint between the two points: (-2,5) and (3,-1). If you coul

Question 93771: will you please explain to me how to do this using an equation. i am so lost.
It says, find the distance and the midpoint between the two points: (-2,5) and (3,-1).
If you could help me, that would be wonderful. thank you and God bless.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"find the distance between the two points: (-2,5) and (3,-1)."

Start with the given distance formula
where

is the first point

and

is the second point

Plug in , , ,

Evaluate to get -5. Evaluate to get 6.

Square each value

Add

So the distance approximates to

which rounds to
7.81

So the distance between (-2,5) and (3,-1) is approximately 7.81 units

"find the midpoint between the two points: (-2,5) and (3,-1)"

In order to find the midpoint, we need to average each corresponding coordinate. In other words, we need to add up the corresponding coordinates and divide the sum by 2.

So lets find the averages between the two points

To find

, average the x-coordinates between the two points

So the x-coordinate of the midpoint is 0.5 (i.e. x=0.5)
-----------------------------------------------------------------------------------------------------------------

To find

, average the y-coordinates between the two points

So the y-coordinate of the midpoint is 2 (i.e. y=2)
-----------------------------------------------------------------------------------------------------------------
Answer:
Since the coordinates of the midpoint are x=0.5, y=2, this means the midpoint is (0.5,2)

Check:
Here is a graph to visually see the answer
Graph of the line segment with the endpoints (-2,5) and (3,-1) with the midpoint (0.5,2)

We could visually verify our answer if we simply draw right triangles from each point like this:

Here we can see that the two triangles are congruent, so our answer is verified.

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