find the relation between X and Y if the points x y 12 and 70 are collinear (by distance formula)
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The relation between x and y is 'x + 3y -7 = 0'
CORRECT QUESTION
Find the relation between X and Y if the points (x,y),(1,2), and (7,0) are collinear (by distance formula)
ANSWER
GIVEN
Collinear points; (x, y),(1,2), and (7,0)
TO FIND
The distance between X and Y by distance formula.
SOLUTION
We can simply solve the above problem as follows-
It is given,
(1,2) and (7,0) are collinear.
Then
Sum of the area of the triangle formed by the given points = 0
Therefore,
1/2 [x1(y2-y1) + x2(y3-y1) +x3(y1-y2)] = 0
Where,
(x1,y1) = (x, y)
(x2,y2) = (1,2)
(x3, y3) = (7,0)
Putting the values in the above formula we get,
= [x(2−0)+1(0−y)+7(y−2)]=0
= [2x−y+7y−14]=0
= 2x+6y−14=0
= x+3y−7=0
Hence, The relation between x and y is 'x + 3y -7 = 0 '
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