Question

What is the perpendicular distance between the line x = 4 and the point M (2, 1)

• A. 4 units
• B. $\frac{1}{2}$units
• C. $\sqrt{2}$ units
• D. 2 units

Answer 1

The correct option is D 2 units

Construct a perpendicular y = 1 to the line x = 4, so that it passes through the point M(2,1).

The 2 lines intersect at, say N, (4,1).

Then the perpendicular distance to the line x=4 from the point M(2,1) is equal to the distance between MN.

Therefore, the perpendicular distance = distance between NM
= $\sqrt{(4-2{)}^2+(1-1{)}^2}$
= $\sqrt{(2{)}^2+(0{)}^2}$
= 2 units

Therefore the perpendicular distance from the point M (2,1) to the
line x = 4 is 2 units.