UPSC NDA Math Model Paper 2

Here, we have to find the value of x such that the lines through the points (- 2, 6) and (x, 8) is perpendicular to the line through the points (3, - 3) and (5, - 9).
Let's find out the slope of the line through the points (3, - 3) and (5, - 9).
As we know that, the slope of the line joining the points (x1,y1) and (x2,y2) is: m=

y2−y1

x2−x1

Here, x1=3,y1=−3,x2=5,y2=−9
⇒m1=

−9−(−3)

5−3

=−3
∵ The lines through the points (- 2, 6) and (x, 8) is perpendicular to the line through the points (3, - 3) and (5, - 9)
So, let the slope of line through the points (- 2, 6) and (x, 8) be m2
⇒−3×m2=−1
⇒m2=1∕3
So, the slope of the line through the points (- 2, 6) and (x, 8) is 1/3
⇒

1

3

=

8−6

x−(−2)

⇒x+2=6
⇒x=4
Hence, option B is the correct answer.