A right triangle is formed by the x-axis, the y-axis, and the line y=3x-7. Find the length of the hypotenuse. Round your answer to the nearest hundredth.
The right triangle is formed by the x-axis, the y-axis and the line y = 3x - 7. The x-axis and the y-axis ate perpendicular to each other. The line y = 3x - 7 intersects the x-axis at the point (7/3, 0) and it intersects the y-axis at the point (0, -7)
The length of the hypotenuse of the triangle formed by these three lines is the distance between the points (7/3, 0) and (0, -7)
That is given by sqrt((7/3)^2 + (-7)^2)
=> sqrt(49/9 + 49)
=> (7/3)sqrt(1 + 9)
The required length of the hypotenuse is 7.378