# Thread: Given ABC, with A(-3,11) B(5,9), C(1,-3). Show, using relevant calculations...

1. ## Given ABC, with A(-3,11) B(5,9), C(1,-3). Show, using relevant calculations...

Given ABC, with A(-3,11) B(5,9), C(1,-3). Show, using relevant calculations, that the segment connecting the midpoints of AB and BC is half the length of AC.

Can someone help me with this question? Would I use the distance formula, midpoint formula? Or...

2. Originally Posted by hamnet
Given ABC, with A(-3,11) B(5,9), C(1,-3). Show, using relevant calculations, that the segment connecting the midpoints of AB and BC is half the length of AC.

Can someone help me with this question? Would I use the distance formula, midpoint formula? Or...
Get the midpoints of AB and BC, using midpoint formula. So have those two new points.
Midpoint of (x1,y1) and (x2,y2) = ((x1+x2)/2,(y1+y2)/2).

Then get the distances of AC and the line segment connecting the two new points, using distance formula.
Distance between (x1,y1) and (x2,y2) = sqrt[(x2-x1)^2 +(y2-y1)^2].

You are asking only how to do it, so there.

3. So the midpoint for AB would be (1,10), while the midpoint for BC would be (3,3).

Using the distance formula for AC I would obtain 14.56021978.

Now what?

4. Originally Posted by hamnet
So the midpoint for AB would be (1,10), while the midpoint for BC would be (3,3).

Using the distance formula for AC I would obtain 14.56021978.

Now what?
Hello,

now you have to calculate the distance between the 2 midpoints and show that this distance is exactly half as long as AC:

$M_{AB}=(1,10)$
$M_{BC}=(3,3)$. Now

$(M_{AB}, M_{BC})=(2,-7)$ which is the half of AC= (4, -14)

EB

5. Originally Posted by hamnet
So the midpoint for AB would be (1,10), while the midpoint for BC would be (3,3).

Using the distance formula for AC I would obtain 14.56021978.

Now what?
Sorry, I saw this only now.

Okay, you got the two midpoints correctly.

Then, like I said, get the distances AC and the line segment coonecting the two midpoints.
You solved only for AC. What about the line segment connecting the two midpoints? Remember, the Question or Problem asks to show that this line segment is half that of AC. And you forgot to get the distance of the line segment? Funny, isn't it?

Anyway, since you got the AC in decimals, then you want to see the distances in decimals. That is fine.

Let us see.

AC = sqrt[(1 -(-3))^2 +(-3 -11)^2]
AC = sqrt[(4)^2 +(-14)^2]
AC = sqrt[16 +196]
AC = sqrt(212)
AC = 14.56021978 --------------yes, you're right.

Line segment connecting midpoints (1,10) and (3,3)
= sqrt[(3-1)^2 +(3-10)^2]
= sqrt[(2)^2 +(-7)^2]
= sqrt[4 +49]
= sqrt(53)
= 7.280109889

Now, is 7.280109889 half of 14.56021978?

If yes, then you showed that the line segment connecting the midpoints of AB and AC is half the length of AC.

6. Oh, yes, I understand now. I do not know why I didn't think of using the distance formula for midpoints AB and BC... Thanks!