Question

Find the value OF A,B,C in
35A
-CB8
_____
183
_____

Answer 1

Answer:

Given: A(a,3),B(2,1) and C(5,a) are collinear.

∴ Slope of AB= Slope of BC

⇒

2−a

1−3

=

5−2

a−1

⇒

2−a

−2

=

3

a−1

⇒−6=(2−a)(a−1)

⇒−6=2a−2−a

2

+a

⇒a

2

−3a−4=0

⇒a

2

−4a+a−4=0

⇒(a−4)(a+1)=0

a=4,−1

For a=4

Slope of BC=

5−2

a−1

=

3

4−1

=

3

3

=1

Equation of BC;(y−1)=1(x−2)

⇒y−1=x−2

⇒x−y=1

For a=−1

Slope of BC=

5−2

a−1

=

3

−1−1

=−

3

2

Equation of BC:(y−1)=−

3

2

(x−2)⇒3y−3=4−2x

⇒2x+3y=7