UPSC NDA Math Model Paper 4

Here, we have to find the value of y such that the line through the points (5, y) and (2, 3) is parallel to the line through the points (9, - 2) and (6, - 5)
Let's find the slope of the line through the points (9, - 2) and (6, - 5)
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=9,y1=−2,x2=6,y2=−5
⇒m=

−5−(−2)

6−9

=1
∵ The line through the points (5, y) and (2, 3) is parallel to the line through the points (9, - 2) and (6, - 5)
So, the slope of the line through the points (5, y) and (2, 3) is also 1.
So, know x1=5,y1=y,x2=2,y2=3 and m=1.
⇒1=

3−y

2−5

⇒−3=3−y
⇒y=6
Hence, option A is the correct answer.