For a right triangle with coordinates (1,4),(4,4),(1,8), explain why both the distance formula and the Pythagorean Theorem can be used to find the length of the hypotenuse.

You can use the distance formula to find the length of the hypotenuse which is the distance between the points (4,4) and (1,8). You can also use the Pythagorean theorem by subtracting 8 from 4 to get 4. Points used are (1,8) and (1,4). You then find the difference between the x values of the points (1,4) and (4,4) which is 3 so now you can solve for the hypotenuse C since you have the lengths of the two legs which are 4 and 3. So you could then use a^2+b^2=c^2 which would then turn into 4^2+3^2=c^2 and you just solve that out to get the length of your hypotenuse.