Q.Find the distance between the points $P(3, 2)$ and $Q(7, 5)$.

This is a direct application of the distance formula — subtract the corresponding coordinates, square, add, and take the square root.

$PQ = \sqrt{(7-3)^2+(5-2)^2} = \sqrt{16+9} = \sqrt{25} = 5$.

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given by

Here $(x_1,y_1)=(3,2)$ and $(x_2,y_2)=(7,5)$, so

The horizontal gap between the points is $4$ units and the vertical gap is $3$ units, and $(3,4,5)$ is a Pythagorean triple, so the straight-line distance works out to exactly $5$ units.

A common slip is subtracting $x_1 - x_2$ in one term but $y_2 - y_1$ in the other (mixing the order); since each difference is squared, the order within a single term does not matter, but students sometimes instead forget to square one of the two differences before adding, or add the differences before squaring.