Final answer:
The length of the hypotenuse of a right triangle formed by the x-axis, the y-axis, and the line y=-2x+4 can be found using the Pythagorean theorem. The length of the hypotenuse is approximately √17 units.
Step-by-step explanation:
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem.
The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the line y=-2x+4 forms a right triangle with the x-axis and the y-axis.
The slope of the line is -2, so the length of the side parallel to the x-axis is 1 (since 2x=2, and x=2/2=1), and the length of the side parallel to the y-axis is 4.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = a² + b²
c² = 1² + 4²
c² = 1 + 16
c² = 17
c = √17
Therefore, the length of the hypotenuse is approximately √17 units.