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if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the...

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cindyloo | Student, Grade 10 | (Level 2) Honors

Posted April 21, 2010 at 8:12 AM via web

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if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the other point?

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neela | High School Teacher | (Level 3) Valedictorian

Posted April 21, 2010 at 11:56 AM (Answer #1)

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Given the midpoint M(0,-3) . One end point is A(0,5). To find the other end point.

Solution:

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).


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krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted April 21, 2010 at 12:27 PM (Answer #2)

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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

Similarly:

y2 = 2y - y1 = 2*(-3) - 5 = - 6 - 5 = - 11

Answer:

The other point is: B(0, -11)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted April 22, 2010 at 12:21 AM (Answer #3)

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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:

xB=2*0-0

xB=0

yB=2*(-3)-5

yB=-6-5

yB=-11

The coordinates of the midpoint are: M(0,-11).

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