if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the other point?
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Given the midpoint M(0,-3) . One end point is A(0,5). To find the other end point.
Given the end points whose coordinates are (x1,y1) and (x2,y2), the mid point is given by ( x1+x2)/2 , (y1+y2)/2. We use this idea when mid point and one end point is known is known.
So M(0,-3 ) = ((x1+x2)/2 , (y1+y2)/2)...(1) Given ( x1, y1) = A(0,5) . To determine (x2,y2). So substituting x1= 0 and y1 = 5 in eq(1), we get:
M(0,3) = ((0+x2)/2 , (5+y2)). Now equate x coordinates on both sides and also do so for y coordinates on both sides:
0 =(0+x2)/2 . Or x2 = 0
-3 =( 5+y2)/2. Or 5+y2 = -6. So y2 = -6-5 = -11.
So (x2,y2) = (0,-11).
The coordinates (x, y) of mid point 'C' of a line AB is given as:
x = (x1 + x2)/2 and
y = (y1 + y2)/2
Where coordinated of the points A and B are:
A(x1, y1) and B(x2, y2)
The question gives coordinates of the mid point (C) and on end of the line (A) as follows:
x = 0
y = -3
x1 = 0
y1 = 5
We have to find coordinates x2 and y2 of point B
x = (x1 + x2)/2
2x = x1 + x2
x2 = 2x - x1 = 2*0 - 0 = 0
y2 = 2y - y1 = 2*(-3) - 5 = - 6 - 5 = - 11
The other point is: B(0, -11)
If we have a midpoint, this one is on the line formed with the points A(0,5) and B(xB,yB).
For finding the coordinates of the midpoint M(xM, yM), we have to solve the system:
xB=2xM-xA, where xM=0 and xA=0
yB=2yM-yA, where yM=-3 and yA=5
Now, we just have to substitute the known values:
The coordinates of the midpoint are: M(0,-11).
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