Question

Which of the following represents the shortest distance between two points $P(a,b)$ and $Q(c,d)$ on a coordinate plane?

• A. $\sqrt{(b-a{)}^2+(d-c{)}^2}$
• B. $(b-a{)}^2+(d-c{)}^2$
• C. $(c-a{)}^2+(d-b{)}^2$
• D. $\sqrt{(c-a{)}^2+(d-b{)}^2}$

Answer 1

The correct option is D $\sqrt{(c-a{)}^2+(d-b{)}^2}$

As per the distance formula, the shortest distance between any two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $\sqrt{(y_2-y_1{)}^2+(x_2-x_1{)}^2}$ .

It is given that the points are $P(a,b)$ and $Q(c,d)$.
So, the shortest distance between the two points $P$ and $Q=\sqrt{(c-a{)}^2+(d-b{)}^2}$.

$\to$ Option A is correct.