SOLUTION: Find the coodinates of the missing endpoint given that S is the midpoint of RT. T(-4,3),S(-1,5)

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Question 213979: Find the coodinates of the missing endpoint given that S is the midpoint of RT.
T(-4,3),S(-1,5)
Found 2 solutions by drj, stanbon:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coordinates of the missing endpoint given that S is the midpoint of RT.
T(-4,3),S(-1,5)

Step 1. Let (x,y) be the endpoint. So the average of the x and y coordinates for the endpoints will be the midpoint. The following steps will show this

Step 2. The x-coordinate for the midpoint S is -1. Then

-1=%28x%2B%28-4%29%29%2F2

%28-1%29=%28x-4%29%2F2

%28-2%29=x-4

x=2


Step 2. The y-coordinate for the midpoint S is 5. Then

5=%28y%2B3%29%2F2

5=%28y%2B3%29%2F2

10=y%2B3

y=7

Step 3. ANSWER: So the endpoint is (2,7)

Step 4. As a check the other endpoint is (-4,3). Then the midpoint is calculated as

%282%2B%28-4%29%29%2F2=-1 so the x-coordinate of the midpoint is -1

%287%2B3%29%2F2=5 so the y-coordinate of the midpoint is 5

The midpoint is then (-1,5) which was given. So it checks out!

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coodinates of the missing endpoint given that S is the midpoint of RT.
T(-4,3),S(-1,5)
------------------------
Let point "R" have coordinates (x,y)
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(x +(-4))/2 = -1
x-4 = -2
x = 2
------------
(y+3)/2 = 5
y+3 = 10
y = 7
---------------
Ans: R is (2,7)
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Note: The coordinates of the midpoint are the average of the
corresponding coordinates of the two endpoints.
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Cheers,
Stan H.