Question

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

Explanation:

Step1: Identify coordinates

The points are $(-2, 4)$ and $(4, 9)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-2, y_1=4, x_2=4, y_2=9$.

$$\begin{align*} d&=\sqrt{(4-(-2))^2+(9-4)^2}\\ &=\sqrt{(6)^2+(5)^2} \end{align*}$$

Step3: Calculate squared terms

Compute squares of the differences.
$\sqrt{36+25}$

Step4: Simplify the radical

Add and simplify the square root.
$\sqrt{61}$

Answer:

$\sqrt{61}$