Question

what is the distance between the points shown on the coordinate plane below? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let the first - point be $(x_1,y_1)=(1, - 1)$ and the second - point be $(x_2,y_2)=(-2,5)$.

Step2: Apply the 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 $x_1 = 1,y_1=-1,x_2=-2,y_2 = 5$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(-2 - 1)^2+(5+1)^2}\\ &=\sqrt{(-3)^2+6^2}\\ &=\sqrt{9 + 36}\\ &=\sqrt{45} \end{align*}$$

\]

Step3: Calculate the value

$\sqrt{45}\approx6.7$

Answer:

$6.7$