Question

find the distance between two points on the coordinate plane
keep going! use the pythagorean theorem to find the distance between each pair of points. round your answer to the nearest hundredth if needed.

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assume first - pair of points

Let's assume for the first pair of points (say $Q(2,0)$ and $P(4,4)$). Here $x_1 = 2,y_1 = 0,x_2=4,y_2 = 4$.
\[

$$\begin{align*} d&=\sqrt{(4 - 2)^2+(4 - 0)^2}\\ &=\sqrt{2^2+4^2}\\ &=\sqrt{4 + 16}\\ &=\sqrt{20}\approx4.47 \end{align*}$$

\]

Step3: Generalize for other pairs

For any two given points on the coordinate - plane, identify their $x$ and $y$ coordinates, substitute into the distance formula, and calculate the square - root value. Round to the nearest hundredth if needed.

Answer:

The distances for each pair of points need to be calculated using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ by identifying the coordinates of the two points in each pair. For example, if the points are $(x_1,y_1)$ and $(x_2,y_2)$, substitute the values and find $d$. Round the result to the nearest hundredth.