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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 - 2}{10 - 5} = \frac{2}{5}$
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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{8 - 4}{20 - 10} = \frac{4}{10} = \frac{2}{5}$
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