UPSC NDA Math Model Paper 5

Here, we have to find the value of a for which the points (- 8, 4), (- 2, 4) and (5, a) are collinear
Let A = (- 8, 4), B = (- 2, 4) and C = (5, a)
Let x1=−8,y1=4,x2=−2,y2=4,x3=5 and y3=a
As we know that, if A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of a ΔABC then area of Δ ABC = | A | where A =

1

2

.|

x1	y1	1
x2	y2	1
x3	y3	1

|
⇒A=

1

2

.|

−8	4	1
−2	4	1
5	a	1

|
⇒A=3a−12
∵ The given points are collinear.
As we know that, if the points A(x1,y1),B(x2,y2) and C(x3,y3) are collinear then area of ΔABC = 0.
⇒A=3a−12=0
⇒k=4
Hence, option A is the correct answer.