Question

If the points a(-1,-4),b(b,c),c(5,-1) are collinear and c=4-2b find the value of b and c

Answer 1

Answer:

Given, A(−1,−4),B(b,c)andC(5,−1)

Two points are said to be collinear if their slopes are equal

⇒ Slope of AB =Slope of BC

We have,

Slope between two points=(

x

2

−x

1

y

2

−y

1

)

⇒

b+1

c+4

=

5−b

−1−c

⇒ (c+4)(5−b)=(−1−c)(b+1)

As we know, 2b+c=4 ⇒ c=4−2b

Substituting this value, we get

⇒ (4−2b+4)(5−b)=(−1−4+2b)(b+1)

⇒ (8−2b)(5−b)=(2b−5)(b+1)

⇒ 40−8b−10b+2b

2

=2b

2

+2b−5b−5

⇒ 10−18b=−3b−5

⇒ −18b+3b=−5−40

⇒ −15b=−45

⇒ b=3 and c=−2