Question

Question Number: 1
Find the value of 'y' if points A, B, and C are collinear: A(-3,-1), B (0.y), and C (3.-9).​

Answer 1

Answer:

Points are P(1,4),Q(3,y) and R(−3,16) are collinear.

Which means area of triangle PQR=0

Area of triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

=

2

1

[1(y−16)+3(16−4)+(−3)(4−y)]

=

2

1

[y−16+3×12−12+3y]

=

2

1

[4y−16+36−12]=

2

1

[4y+8]

Since points are collinear:

2

1

(4y+8)=0

or y=−2.

Answer 2

Answer:

x1=-3

x2=0

X3=3

y1=-1

y2=y

y3=-9

For points to be collinear

x1(y2-y3)+x2(y3-y2)+x3(y1-y2)

-3(-1-(-9))+0(-9-y)+3(-1-y)=0

-3(-1+9)+0-3-3y=0

-3(8)-3-3y=0

-24-3-3y=0

-27-3y=0

-3y=27

y=-9