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 coordinates

First, find the coordinates of the two points. Let's assume the left point is \((x_1, y_1)\) and the right point is \((x_2, y_2)\). From the graph, the left point is at \((-1, -4)\) and the right point is at \((7, -2)\).

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 \(x_1 = -1\), \(y_1 = -4\), \(x_2 = 7\), \(y_2 = -2\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(7 - (-1))^2 + (-2 - (-4))^2}\\ &=\sqrt{(8)^2 + (2)^2}\\ &=\sqrt{64 + 4}\\ &=\sqrt{68} \end{align*}$$

\]

Step3: Calculate and round

Calculate \(\sqrt{68}\approx 8.246\), then round to the nearest tenth, which is \(8.2\).

Answer:

\(8.2\)