# The Distance Between Vertices

[SOLVED] The Distance Between Vertices

## Homework Statement

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?

## 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.

## The Attempt at a Solution

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Hootenanny
Staff Emeritus
Gold Member
Side AC = 5
No it isn't.
The midpoint of AB is at (-1,0)
Correct
The distance from the midpoint of AB to C = 5
No it isn't.
It's the same as AC.
Correct

symbolipoint
Homework Helper
Gold Member
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).

Hootenanny
Staff Emeritus
Gold Member
Use the distance formula to find the length from point C (-1, 0) to the point (0, 5).
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).

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).
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?

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

Now you're just making things up.

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

Now you're just making things up.
It's what the calculator indicated:

5.097019514 to be exact

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

Hootenanny
Staff Emeritus
Gold Member
It's what the calculator indicated:

5.097019514 to be exact

I'm lost.
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.

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

Have I done any other calcs correctly?

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

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...

Hootenanny
Staff Emeritus
Gold Member
I rounded it. I didn't round up to 5.1. I rounded down to 5.

Have I done any other calcs correctly?

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

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.
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.

Hootenanny
Staff Emeritus
Gold Member
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.
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.

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.
Thank you