The length is 7.8 inches.
The longest side of a right triangle is the hypotenuse. The endpoints of the hypotenuse are at (-3, -2) and (2, 4). We will use the distance formula:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(4--2)^2+(2--3)^2}
\\
\\=\sqrt{6^2+5^2}=\sqrt{36+25}=\sqrt{61}=7.8[/tex]
