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प्रश्न
If the points A(−2, 1), B(a, b) and C(4, −1) are collinear and a − b = 1, find the values of a and b.
उत्तर
The given points are A (−2, 1), B (a, b) and C (4, −1).
Since the given points are collinear, the area of the triangle ABC is 0.
`=>1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0`
Here, `x_1=-2, y_1=1, x_2=a, y_2=b and x_3=4, y_3=-1`
`therefore 1/2[-2(b+1)+a(-1-1)+4(1-b)]=0`
-2b-2-2a+4-4b=0
2a+6b=2
a+3b=1 ........(1)
Given :
a-b=1 ..............(2)
Subtracting equation (1) from (2), we get:
4b=0
b=0
Substituting b = 0 in (2), we get:
a=1
Thus, the values of a and b are 1 and 0, respectively.
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