Question

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.a. Use the midpoint formula.b. The length of the hypotenuse is the square root of 20.c. Use the distance formula.d. Find the slope.e. The length of the hypotenuse is the square root of 41.f. Use the Pythagorean theorem.g. The length of the hypotenuse is 3.h. Not possible.

Answer 1

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;

`\begin{gathered} 1)\text{ using the distance formula} \\ D=√((x_2-x_1)^2+(y_2-y_1)^2) \\ D=√((-3-1)^2+(-3-2)^2) \\ D=√((16+25)) \\ D=√(41) \\ Hypotenuse\text{ =}√(41) \end{gathered}`
`\begin{gathered} 2)\text{ Pythagorean theorem} \\ The\text{ length of the other legs are;} \\ 4\text{ and 5 using the distance formula} \\ \end{gathered}`

Thus;

`\begin{gathered} 4^2+5^2=hypotenuse^2 \\ hypotenuse=√(16+25) \\ hypotenuse=√(41) \end{gathered}`

Answer;

`\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}`