Question

If the point A(-1,-4) B (b, c) C(5,-1) are collinear and 2b+c=4. find the value of B and C

Answer 1

Step-by-step explanation:

three points (x1, y1), (x2, y2) and (x3, y3) are collinear then [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)] = 0. A( -1, -4),B(b,c) and C(5, -1) are collinear then [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)] = 0. ⇒ [ -1( c + 1) +b( -1 + 4) + 5(-4 - c)] = 0. ⇒ [ - c - 1 -b + 4b - 20 - 5c] = 0. ⇒ [3b - 6c] = 21 ⇒ b - 2c = 7 -------(1) Given 2b + c = 4 -------(2) solving (1) and (2) we get b = 3 and c = -2.

Answer 2

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