In a co-ordinate system , if three points (5,3)(x,y) and (3,2)lie on a same line ,fine the value of X.
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Md.Nazrul Islam
- Senior | Next Rank: 100 Posts
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If the 3 points lie on the same line, they are collinear.
For 3 points to be collinear, the slope of 2 points taken at a time will be equal.
A(5,3), B(x,y), C(3,2)
slope for 2 points(x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1)
Slope m1 = (y-3)/(x-5)
slope m2 = (2-y)/(3-x)
m1 = m2 as they lie on the same line.
(y-3)/(x-5) = (2-y)/(3-x)
==> (y-3)(3-x) = (2-y)(x-5)
==> 3y - 9 -xy +3x = 2x - 10 - xy + 5y
==> x + 1 = 2y-------(eqn 1)
slope of AC = m3 = (2-3)/(3-5)
m3 = -1/-2
m3 = 1/2
from eqn 1, x = 2y - 1
giving values for y, we can get values for x.
y = 0, x = -1
y = 1, x = 1
y = 2, x = 3
and so on...
