if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the other point?
4 Answers
hkj1385 | (Level 1) Assistant Educator
Let the other point be (x,y)
Now, mid-point of (x,y) &(0,5) will be
[{(x+0)/2},{(y+5)/2}]
Given
{(x+0)/2} = 0
thus, x = 0
Also,
{(y+5)/2} = -3
or, y + 5 = -6
or, y = -11
Hence the required point (x,y) is (0,-11)
giorgiana1976 | College Teacher | (Level 3) Valedictorian
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).
krishna-agrawala | College Teacher | (Level 3) Valedictorian
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)
neela | High School Teacher | (Level 3) Valedictorian
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).