Q: what is length triangle mean?

it means what is the length of the triangle

Q: lowkey brain screaming - im still somewhat confused

The midpoint formula is just an average. Add the 2 X-values, then divide by 2. Add the 2 Y-values, then divide by 2. You have then found the average for the X and Y values which gives you the point half way between the original 2 points.

Question 1

How do you find the endpoint of a line when you are given the other endpoint and the midpoint?

Accepted Answer

Great question, and it's definitely a situation we need to be able to solve.

When we are *given the Midpoint and an Endpoint, and asked to find the _Other Endpoint*_.

We can still *use the concepts from the Midpoint Formula* _by plugging in the information we do have_, because…

we normally _find the Midpoint_ by adding the corresponding coordinates, then dividing by two…

(first endpoint + second endpoint) divided by two = Midpoint

So, we know that…
(*x1 + x2)/2 = Midpoint x*
and that…
(*y1 + y2)/2 = Midpoint y*

*the given Endpoint (x, y) can be plugged into _either the first or second_ x and y* locations because addition is Commutative, (it's rearrangeable), so it doesn't matter which end values are first or second,

and *the given Midpoint, (x or y), is placed as equal* to the Endpoint addition then division.

Given:
*Endpoint (3, 5)
Midpoint (7, 10*)

•Find _Other_ Endpoint
=
(x1 + x2)/2 = Midpoint x
and
(y1 + y2)/2 = Midpoint y
=
(*x + 3)/2 = 7*
and
(*y + 5)/2 = 10*

•Let's solve for x first:
(*x + 3)/2 = 7*
_Multiply both sides by 2_,
to cancel the division on the left.
=
*2*((x + 3)/2) = 7 • *2*
=
*x + 3 = 14*
_Subtract 3 from both sides_,
to isolate x on the left.
=
x + 3 -3 = 14 -3
=
*x = 11* ←🥳

•Solve for y the same way…
(*y + 5)/2 = 10*
=
2((y + 5)/2) = 10(2)
=
*y + 5 = 20*
=
*y = 20 -5*
=
*y = 15* ←🥳

• Other Endpoint is at:
(*11, 15*) ←🥳🥳

•Each time the pattern of operations _will be the same_:
_*Multiply_ the Midpoint coordinate by 2, then _add or subtract_ the given Endpoint* to isolate variable.

*2 • (Midpoint x or y) +/- (endpoint)
=
other endpoint*

•Be aware if a given Endpoint *coordinate is negative, it will be added* rather than subtracted to isolate the variable.

(*Example in Comments*)

(ㆁωㆁ)I hope this helps someone!

Question 2

I think I might have lost a few braincells in the process
...   :[

Accepted Answer

Don't worry- you are not the only one X) This was supposed to make me smarter T_T

Question 3

don't u divied when u do the midpoint

Accepted Answer

You are finding the average, so one way is to add the two x coordinates and divide by 2, then do the same for the y coordinates.

Question 4

how do i find coordinators if im looking for the endpoint

Accepted Answer

Are you saying you know one endpoint and the midpoint? If this is what you are asking, find the vector from the endpoint to the midpoint, the starting at midpoint, go along an equivalent vector. For example, endpoint is at (5,6) and midpoint is at (3,8) so the vector is <3-5, 8-6> or <-2,2>. SO starting at (3,8) along vector <-2,2), you end at (1,10).

Question 5

what is length triangle mean?

Accepted Answer

it means what is the length of the triangle

Question 6

lowkey brain screaming - im still somewhat confused

Accepted Answer

The midpoint formula is just an average.  
Add the 2 X-values, then divide by 2.
Add the 2 Y-values, then divide by 2.
You have then found the average for the X and Y values which gives you the point half way between the original 2 points.

Course: Geometry (all content) > Unit 15

Midpoint formula review

What is the midpoint formula?

What problems can I solve with the midpoint formula?

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