Question

find the length of a segment with an endpoint of (2,5) and a midpoint of (5,9)

Answer 1

If you know an endpoint and a midpoint, you know that the length is 2x the distance between the endpoint and the midpoint, right?

To find the distance between two points \((x_1,y_1),(x_2, y_2)\) use the formula \[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

It doesn't matter which point you decide is which.

Answer 2

is the answer 7

Answer 3

?

Answer 4

You tell me.

Answer 5

How did you arrive at that answer?

Answer 6

lol im asking you, am i correct?

Answer 7

i recheck my answer is the correct answer 5?

Answer 8

Show me or describe your work, and I'll tell you if you did it correctly.

Answer 9

okay using the distance formula that you give me

Answer 10

\[d = (x1 - x2) ^{2} + (y1 - y2)^{2 }\]

Answer 11

\[( 2- 5) ^{2 } (5-9)^{2}\]

Answer 12

Okay, good. So the distance from the midpoint to the endpoint is 5. What is the length of the entire segment?

Answer 13

\[(-3)^{2} (-4)^{2}\]

Answer 14

10

Answer 15

There you go! It's just twice the distance from the midpoint to the endpoint.

Answer 16

thanksssss!

Answer 17

Think of it as a diameter of a circle and a radius. The radius is the distance from the edge to the center, and that's what we found. The diameter is the distance from the edge through the center to the other edge, and that's what we got at the end.

Answer 18

true true, math really isnt my thing

Answer 19

In a real life situation, if I told you to put a ruler down so the center was on the midpoint, and an end was on the endpoint, I'm sure you would immediately realize that the answer was twice the distance you'd measured. But doing it on the coordinate grid with a formula, you don't have that natural instinct of how it works at first.

Answer 20

could you help me with my next question

Answer 21

I can try, before I see it, I can't know for sure :-)

Answer 22

find the midpoint of a segment whose endpoints are (5,8) and (-3,10)

Answer 23

Okay, do you know the formula for a midpoint given the two endpoints?

Answer 24

no

Answer 25

Are you ready to figure it out? :-)

Answer 26

yesss, you not willing to give me the answer?

Answer 27

Okay, let's figure it out!

Suppose we have two points on a number line. One point is at x = 7, the other is at x = 3. What is the distance between them, and what is the point midway between them?

Answer 28

5 and im guessing midway is 2.5

Answer 29

Let me draw a picture:
How many points do you have to move to the right to go from 3 to 7?

Answer 30

4

Answer 31

Okay, what's half of 4? If you move that many points to the right from 3, or to left from 7, what point do you end up with?

Answer 32

2

Answer 33

Okay, so what point?

Answer 34

at 5

Answer 35

Right! What we did was take (7-3) to get the distance between them, and then we divided that in half and added it to one of the points to get the midpoint. Another way to do it would be to add the two points, and then divide by 2. That turns out to be the same thing. (7+3)/2 = 5.

Answer 36

im lost

Answer 37

i get it

Answer 38

sorry

Answer 39

Not a problem. Do you agree that we just took the average of the two points?

Answer 40

huh ? so in my case i would have to add 5 and 8 then divide by 2

Answer 41

then add -3 and 10 then divide by 2

Answer 42

No, not quite, you added the x and y values together, but you want to add x values to x values, and y values to y values. The midpoint is just the average of the x values, the average of the y values.

Answer 43

Think of it as doing each direction separately. You find the halfway point on the x-axis, and the halfway point on the y-axis, and then where the lines through those points drawn perpendicular to the axes cross is the midpoint.

Answer 44

okay

Answer 45

So what are your two x values from your points? Add them together, and divide by 2. That's the x value of the midpoint.

Answer 46

Similarly, take the two y values, add them together,divide by 2, and that's the y value of the midpoint.

Answer 47

5 and -3 right?

Answer 48

the answer at the end would come out to 1,9 right?

Answer 49

Yes!

Answer 50

yay, we did it

Answer 51

And if you think about it, if we had two points on the x-axis (both y values are 0), we get exactly the same result, because we average 0 and 0 and get 0. Similarly, if both x values are the same, we just average the y values.

Answer 52

Does the formula make sense to you?

Answer 53

thanksss, are you a teacher or something? get get it the end you saying now. but the way we slove the problem

Answer 54

* i dont understand the way your saying it now. but the way we slove the problem sounds easier to me

Answer 55

Midpoint (M) of \((x_1,y_1),(x_2,y_2)\):

\[(\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2))\]

Answer 56

Here's a real-life application of this that I learned long ago in mechanical drawing class. Suppose you have a box, and you need to draw a line right down the middle. How can you do that? Well, you take your ruler, and you put it diagonally across the box. Move the ruler so that there are an even number of units between the spots on the ruler where it crosses the edges. Say, 2 and 8, for example. Make a mark at the halfway point on the ruler (on the box). Now go somewhere else on the box, and repeat the process. Any diagonal line works, just mark the midpoint. Now you lay down the ruler between the two points you marked, draw a straight line, and you've got your midline!

Answer 57

Much faster and more accurate than trying to figure out what half of 3.92543 inches is, and then measuring off that distance from one side in a couple of places.

Answer 58

I'm not a teacher, but I enjoy helping others learn, especially when I can see the little light bulb go on in their head as they understand something for the first time :-)

Answer 59

awww, you should be

Answer 60

could you help with the question i just posted