UPSC NDA I 2021 Mathematics Solved Paper

Concept:
The equation of a line passing through the point (x1,y1) and having the slope ' m ' is given as:
y−y1=m⋅(x−x1)
Calculations:
Given: The point of intersection of diagonals of a square ABCD is at the originand one of its vertices is at A(4,2).
So, the diagonal AC passes through the origin
As we know that, the slope of the line joining the points (x1,y1) and (x2,y2) is: m=‌

y2−y1

x2−x1

The slope of line AC is givenby
‌

2−0

4−0

=‌

1

2

In square ABCD, the diagonals AC and BD are perpendicular to each other.
⇒ Slope of AC× slope of BD=−1
So, the slope of BD is −2.
As we know that, the equation of a line passing through thepoint (x1,y1) and having the slope ' m ' is given as:
y−y1=m⋅(x−x1)
The equation of BD whose slope is - 2 and passes through origin is given by:
y−0=(−2)⋅(x−0)
⇒2x+y=0
Hence, the correctoption is 1 .