Question

what is the approximate distance between points p and q? round your answer to the nearest hundredth.
a. 4 units
b. 4.12 units
c. 4.89 units
d. 5.1 units

Explanation:

Step1: Identify coordinates

Assume $P(x_1,y_1)$ and $Q(x_2,y_2)$. From the graph, if we estimate the coordinates, say $P(-3, - 4)$ and $Q(2,-3)$.

Step2: Apply distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1=-3,y_1 = - 4,x_2=2,y_2=-3$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(2-(-3))^2+((-3)-(-4))^2}\\ &=\sqrt{(2 + 3)^2+(-3 + 4)^2}\\ &=\sqrt{5^2+1^2}\\ &=\sqrt{25 + 1}\\ &=\sqrt{26}\approx5.10 \end{align*}$$

\]

Answer:

D. 5.1 units