UPSC NDA Math Model Paper 6

Here, 5

^

i

−2

^

j

,8

^

i

−3

^

j

,a

^

i

−12

^

j

Let, A = (5, -2), B = (8, -3), C = (a, -12)
Now, slope of AB = Slope of BC = Slope of AC ....(∵ points are collinear)

−3−(−2)

8−5

=

−12−(−3)

a−8

⇒

−1

3

=

−9

a−8

⇒ a - 8= 27
⇒ a = 27 + 8 = 35
Hence, option (4) is correct.