# The Distance Between Vertices

1. Apr 28, 2008

### LLS

[SOLVED] The Distance Between Vertices

1. The problem statement, all variables and given/known data

A triangle has vertices at points A, B and C, which are located at (1,0), (-3,0), and (0,5) respectively. What is the distance from the midpoint of AB to point C?

2. Relevant equations

3. The attempt at a solution

I plotted the triangle. Side AC = 5

The midpoint of AB is at (-1,0)

The distance from the midpoint of AB to C = 5. It's the same as AC.

I think that I am missing something.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 28, 2008

### Hootenanny

Staff Emeritus
No it isn't.
Correct
No it isn't.
Correct

3. Apr 28, 2008

### symbolipoint

You correctly chose that the midpoint of AB is (-1, 0); but AC is not equal to 5.

Point C is at (0, 5). Use the distance formula to find the length from point C (-1, 0) to the point (0, 5).

4. Apr 28, 2008

### Hootenanny

Staff Emeritus
I'm sure symbolipoint means,

Use the distance formula to find the length from the midpoint of AB (-1, 0) to the point C (0, 5).

5. Apr 28, 2008

### LLS

c^2 = (5-0)^2 + (1-0)^2

c^2 = 25 + 1 = 26

c = 5.097

I still get that the distance = 5.

What did I do wrong?

6. Apr 28, 2008

### Hootenanny

Staff Emeritus
How is $\sqrt{26} = 5.097... =5$ :surprised?

Now you're just making things up.

7. Apr 28, 2008

### LLS

It's what the calculator indicated:

5.097019514 to be exact

I'm lost. Did I do the distance formula calc correctly?

8. Apr 28, 2008

### Hootenanny

Staff Emeritus
All I'm say is that 5.097019514.... is NOT the same as 5! Therefore, you distance from the midpoint of AB to C is NOT 5.

9. Apr 28, 2008

### LLS

I rounded it. I didn't round up to 5.1. I rounded down to 5.

Is 5.097019514 the correct answer?

Have I done any other calcs correctly?

Please steer me towards a calc that works. I don't want to give up.

10. Apr 28, 2008

### tron_2.0

its best if you do not plug in numbers in until the very end. for instance leave sqrt(5) as sqrt(5) and do not put it down as 5.097...

11. Apr 28, 2008

### Hootenanny

Staff Emeritus
Your calculation is correct, your final answer is not. If you are rounding then you should explicitly state the degree of accuracy to which you have quoted the answer. However an exact answer is always preferable, you should leave it in surd form unless instructed otherwise.

12. Apr 28, 2008

### LLS

Was it the correct calculation? I may have a correct calculation but if the formula was wrong or the values the answer is wrong.

I'm really confused as to what the answer is.

13. Apr 28, 2008

### Hootenanny

Staff Emeritus
The formula is correct and the answer is $\sqrt{26}$ as you calculated, there is no need to write it in decimal form (unless stated otherwise). An answer in this form is exact, as opposed to an approximated decimal.

However, if you do wish to write it in decimal form, you must state explicitly the degree of accuracy which you are rounding it to. Simply writing AB=5 is incorrect, but writing AB=5 (1sf) is acceptable.

14. Apr 28, 2008

### LLS

Thank you

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