UPSC NDA Math Model Paper 8

Using the formula for the distance, the distance between the point (2, -1) and the line x + y - 2 = 0 will be:
Distance =

|1(2)+1(−1)−2|

√12+12

=

1

√2

Since this distance is the height (h) of the equilateral triangle, we can calculate its side (a) as follows:
h=

√3

2

a
⇒

1

√2

=

√3

2

a
⇒a=

1

√2

×

2

√3

=

1

√2

×

√2×√2

√3

=√

2

3

∴ The length of the side of the equilateral triangle is √

2

3

.