Question: Finding Distance on the Coordinate Plane
What is distance between point $X$ and point $Y$?
$\sqrt{11}$
$\sqrt{22}$
$\sqrt{61}$
$\sqrt{72}$
position_hint=top-left: A coordinate plane graph shows points $X$ at $(-2, 4)$ and $Y$ at $(3, -2)$ connected by a diagonal segment; a dashed horizontal from $X$ to $Z$ at $(3, 4)$ and a dashed vertical from $Z$ down to $Y$ form a right triangle.
1. **State the problem:** Find the distance between points $X(-2,4)$ and $Y(3,-2)$ on the coordinate plane.
2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula derived from the Pythagorean theorem:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
3. **Calculate the differences:**
$$x_2 - x_1 = 3 - (-2) = 3 + 2 = 5$$
$$y_2 - y_1 = -2 - 4 = -6$$
4. **Substitute into the formula:**
$$d = \sqrt{5^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61}$$
5. **Interpretation:** The distance between points $X$ and $Y$ is $\sqrt{61}$.
**Final answer:** $\boxed{\sqrt{61}}$