In the $xy$-plane, what is the distance between the points $Q(-2, -3)$ and $R(4, 1.5)$?

Construct a right triangle with hypotenuse $QR$ by dropping a vertical line from $R$ and a horizontal line from $Q$. The legs of the triangle have lengths: - Horizontal: $4 - (-2) = 6$. - Vertical: $1.5 - (-3) = 4.5$. By the Pythagorean theorem, $QR = \sqrt{6^{2} + 4.5^{2}} = \sqrt{36 + 20.25} = \sqrt{56.25} = 7.5$. - Trap A ($4.5$) and Trap B ($6$) each give a *leg* length, not the hypotenuse. - Trap D doubles the correct value. The distance formula $d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$ is just the Pythagorean theorem applied to coordinates.