Question

It says Graph a Right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.(4,4) and (-4,2) I've shown the photo and it wants me to find Leg 1, Leg 2 and the hypotenuse I've already made an attempt to solve it and it was wrong.

Answer 1

`\begin{gathered} Hypothenuse=2\sqrt[]{17} \\ \text{base}=8 \\ \text{height}=2 \end{gathered}`

Step by step explanation:

To calculate the hypotenuse of the triangle, we are going to use the distance between points formula. It is represented by the following expression:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Then, with the points (-4,2) and (4,4)

`\begin{gathered} d=\sqrt[]{(4-(-4))^2+(4-2)^2} \\ d=\sqrt[]{8^2+2^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=2\sqrt[]{17} \end{gathered}`

Then, for the legs:

coordinates for the base (-4, 2) and (4,2)

`\begin{gathered} \text{base}=\sqrt[]{(4-(-4))^2+(2-2)^2} \\ \text{base}=\sqrt[]{64} \\ \text{base}=8 \end{gathered}`

for the height: (4,2) and (4,4)

`\begin{gathered} \text{height}=\sqrt[]{(4-4)^2+(4-2)^2} \\ \text{height}=\sqrt[]{2^2} \\ \text{height}=2 \end{gathered}`