Question

What is the slope of the hypotenuses of the triangles in simplest form? First-quadrant graph showing a ray through the origin and the points (5, 2), (10, 4), and (20, 8). Two triangles each have hypotenuses with endpoints along the line, a vertical leg, and a horizontal leg. The first triangle has a hypotenuse with endpoints at (5, 2) and (10, 4). The second triangle has a hypotenuse with endpoints at (10, 4) and (20, 8).

Answer 1

`m = (y_(2) - y_(1))/(x_(2) - x_(1)) = (4 - 2)/(10 - 5) = (2)/(5)`
y - y₁ = m(x - x₁)
y - 2 = ²/₅(x - 5)
y - 2 = ²/₅(x) - ²/₅(5)
y - 2 = ²/₅x - 2
+ 2 + 2
y = ²/₅x


`m = (y_(2) - y_(1))/(x_(2) - x_(1)) = (8 - 4)/(20 - 10) = (4)/(10) = (2)/(5)`
y - y₁ = m(x - x₁)
y - 4 = ²/₅(x - 10)
y - 4 = ²/₅(x) - ²/₅(10)
y - 4 = ²/₅x - 4
+ 4 + 4
y = ²/₅x