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प्रश्न
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
उत्तर
As the given points are collinear, so the area of the triangle formed by them must be 0.
∴ 1/2[x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)] = 0
Here, x1= −1 , y1= −4, x2= b, y2= c, x3= 5, y3= −1
∴12[−1(c+1)+b(−1+4)+5(−4−c)]=0
⇒−c−1−b+4b−20−5c=0
⇒−6c+3b−21=0
⇒b−2c=7 ...(1)
Given:
2b+c=4 ...(2)
On solving equation (1) and (2), we get:
b=3 and c=−2
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