Step 1
Given; A triangle has vertices at (-3,-3) ,(-3,2) and 1,2.
Choose from the following all the possible ways to find the length of the hypotenuse of the triangle. Then calculate the actual length. Select all correct answers; more than one answer may be correct.
Step 2
The image of the triangle is seen below.
Thus, we can find the length of the hypotenuse by;
[tex]\begin{gathered} 1)\text{ using the distance formula} \\ D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt{(-3-1)^2+(-3-2)^2} \\ D=\sqrt{(16+25)} \\ D=\sqrt{41} \\ Hypotenuse\text{ =}\sqrt{41} \end{gathered}[/tex][tex]\begin{gathered} 2)\text{ Pythagorean theorem} \\ The\text{ length of the other legs are;} \\ 4\text{ and 5 using the distance formula} \\ \end{gathered}[/tex]Thus;
[tex]\begin{gathered} 4^2+5^2=hypotenuse^2 \\ hypotenuse=\sqrt{16+25} \\ hypotenuse=\sqrt{41} \end{gathered}[/tex]Answer;
[tex]\begin{gathered} C)\text{ use the distance formula.} \\ E)\text{ The length of the hypotenuse is square root of 41.} \\ F)\text{ Use the Pythagorean theorem.} \end{gathered}[/tex]
