Chapter 9, Problem 1CR

To determine

To calculate: To find the distance between PQ

Answer to Problem 1CR

Distance PQ is option d. $2\sqrt{5}$

Explanation of Solution

Given:

  $\begin{array}{l}P=(-4,3)\\ Q=(-6,-1)\end{array}$

Formula Used:

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the Pythagorean theorem:

  $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation:

Say distance between PQ = d

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(-6-(-4)\right)}^2+{\left(-1-3\right)}^2}\\ d=\sqrt{{\left(-6+4\right)}^2+{\left(-4\right)}^2}\\ d=\sqrt{{\left(-2\right)}^2+{\left(-4\right)}^2}\\ d=\sqrt{4+16}\\ d=\sqrt{20}\\ d=2\sqrt{5}\end{array}$

Therefore, distance PQ = $2\sqrt{5}$

Conclusion:

Distance PQ is option d. $2\sqrt{5}$