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

Mark me as brainliest

Answer 2

Answer:

$\red { Value \: of \: b }\green {=3}$

$\red { Value \: of \: c }\blue {= -2}$

Step-by-step explanation:

$Let \: A(-1,-4) = (x_{1},y_{1}),\\B(b,c) = (x_{2},y_{2}),\\C(5,-1) = (x_{3},y_{3})$

$Area \: of \: \triangle ABC = 0 \: (A,B\:and \:C \:are \: collinear)$

$\implies |x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})| = 0$

$\implies | (-1)[c-(-1)]+b[-1-(-4)]+5[-4-c]| = 0$

$\implies | -1(c+1)+b(-1+4)+5(-4-c)|=0$

$\implies | -c-1-b+4b-20-5c| = 0$

$\implies -6c+3b-21=0$

/* Divide each term by 3 ,we get

$\implies -2c+b -7 = 0$

$\implies b -2c = 7 \: ---(1)$

$2b + c= 4 \: ---(2) \:(given )$

/* Multiply equation (2) by 2 and add with eqution (1), we get

$\implies 5b = 15$

$\implies b = \frac{15}{5} = 3$

/* Put b = 3 in equation (2) ,we get

$\implies 2\times 3 + c = 4$

$\implies 6 + c = 4 \\\implies c = 4 - 6 = -2$

Therefore.,

$\red { Value \: of \: b }\green {=3}$

$\red { Value \: of \: c }\blue {= -2}$

•••♪