Question

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

• A. 1/2 units
• B. √2 units
• C. 2 units
• D. 4 units

Answer 1

The correct option is C

2 units

The y coordinate of M (2, 1) is 1.

So we construct a line y = 1 perpendicular to the line x = 4.

x = 4 and y = 1 intersect at, the point 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.