Question

How do i find the missing coordinate when im given one coordinate and the midpoint.
M=(-1,1) and P=(2,4)

Answer 1

Use the midpoint formulas.

The x-coordinate of the midpoint is given by:\[\Large M_x=\dfrac {x_{1}+x{2}}{2}\]So plug in \(\Large M_x\text{ and }{x_{1}}\), which you were given, and solve for \(\Large {x_{2}}\)

Then do similarly for the y coordinate.

Answer 2

im sorry that doesn't make sense to me :(

Answer 3

Do you know the midpoint formula? If you have 2 points, do you know how to find their midpoint?

Answer 4

yes

Answer 5

\[\Large \left( \dfrac {x_{1}+x{_2}}{2}, \dfrac {y_{1}+y_{2}}{2} \right)\]

Answer 6

yeah i know that formula but i dont understand how to use it to find the other point

Answer 7

OK then, take just the x coordinate of the midpoint first. It is found by:

\[\Large xmid=\dfrac {x_{1}+x{2}}{2}\] where i'm just using "xmid" to mean the x coordinate of the midpoint.

Answer 8

Now, you're GIVEN the midpoint, so you know xmid, right? And you're GIVEN one point, so you know \(x_{1}\) because it's the x-coordinate of the known point.

So plug those KNOWN values into that expression for xmid. then solve for \(x_{2}\)

Answer 9

yeah i got -1= 2+x/2

Answer 10

ok, good....
\[\Large -1=\dfrac {2+x}{2}\]

Now solve that puppy for x!

Answer 11

am i supposed to multiply -1 and 2

Answer 12

Well, what should you do FIRST. take it one step at a time. How can you eliminate that fraction on the right side?

Answer 13

Divide 2 and 2 so im left with -1=x?

Answer 14

noooo.....

Answer 15

if a=b/c

Then ca=b

Answer 16

IM SO LOST! :(

Answer 17

So you clear a denominator of a fraction by MULTIPLYING by that denominator. Not dividing!

Answer 18

so i should get -1=4+x

Answer 19

Hang in there. I know you're frustrated but this is basic math and it's important that you work to wrap your head around it.

Answer 20

does x=4?

Answer 21

No. Two problems.
1. when you do ANYTHING on one side, you have to do it on the OTHER side too. You changed something on the right but didn't do anything on the left.
2. The numerator of the fraction is a whole term, that WHOLE THING is divided by 2. So when you multiply by 2, it cancels the den'r, but there's no "multiplying" in the numerator - it just cancels out

\(\Large 2\cdot(-1)=\dfrac {2+x}{2}\cdot2\)

Answer 22

And no, not x=4

Answer 23

so im using the denominator when i multiply both sides?

Answer 24

when i multiply the fraction do i multiply both twos by two?

Answer 25

Here's an example with different expressions:

\(\Large 3=\dfrac {1+x}{5}\) I want to clear that den'r of 5, so I multiply both sides by 5.

\(\Large 5\cdot(3)=\dfrac {1+x}{5}\cdot5\) On right side, the five in den'r completely cancels with the 5 I'm multiplying by

\(\Large 15={1+x}\)

Answer 26

ok that makes more sense

Answer 27

so right now i got -2=2+x

Answer 28

no, here's why:

\(\Large \dfrac {a}{b}\cdot b=a\)

The WHOLE NUMERATOR is a.... whether it's a single number, a single variable, a sum or algebraic expression. The WHOLE NUMERATOR is one "unit" over the den'r, which cancels.

Answer 29

GOOD!!

Answer 30

Now you have

-2=2+x

So what's x? What do you do now?

Answer 31

do i divide both sides by 2?

Answer 32

No, no need to divide. You divide to undo a PRODUCT (multiplication). You don't have a product to deal with. You have a SUM (2+x). You need to get that 2 to the other side. What operation will "undo" a sum?

Answer 33

subtraction

Answer 34

Yes! Subtract 2 from both sides, to get the 2 to go "from" the right side "to" the left side. What do you get?

Answer 35

x=0?

Answer 36

Careful... you have a negative number on that left side. You are SUBTRACTING from a NEGATIVE.

-2-2=?

Answer 37

oh its -4 and for y i got -2.....is that correct? (-4,-2)

Answer 38

YES!! Hooray!! :)

Answer 39

alright thanks so much :)

Answer 40

You're welcome. :) Good job sticking with it. Doesn't it feel good to have figured it out? :)

Answer 41

yup :D