Chapter 10.2, Problem 1QR

To determine

To find: The distance between $P$ and $Q$ .

Answer to Problem 1QR

The answer is: $(2,3)$

Explanation of Solution

Given information:

The values of

  $\begin{array}{c}P=(1,2)\\ Q=(5,3)\end{array}$

Calculation:

Know that the component form of the vector from point $\left(x_1,y_1\right)$ to point $\left(x_2,y_2\right)$ is equal to:

  $(x_2-x_1,y_2-y_1)$

The component form of the vector from the origin to the point $A=(2,3)$ is equal to, according to the previous results.

  $(2-0,3-0)=(2,3)$

Therefore, the required distance between $P$ and $Q$ is $(2,3)$ .