Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates

First, we find the coordinates of the two points. From the graph, the yellow point on the right is at \((7, 3)\) and the yellow point at the bottom is at \((-2, -9)\).

Step2: Apply the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substituting \(x_1 = 7\), \(y_1 = 3\), \(x_2 = -2\), and \(y_2 = -9\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(-2 - 7)^2 + (-9 - 3)^2}\\ &=\sqrt{(-9)^2 + (-12)^2}\\ &=\sqrt{81 + 144}\\ &=\sqrt{225}\\ &= 15 \end{align*}$$

\]

Answer:

The distance between the two points is \(\boxed{15}\).