Right triangle from axes

A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?

Correct answer:

k₁ = -0.0149
k₂ = -10.7051

Step-by-step explanation:

S = 36 S = \frac{a b}{2} a b = 2 \cdot 36 = 72 k = \frac{2 - b}{5 - a} = - \frac{b}{a} (2 - b) a = - b \cdot (5 - a) (2 - 72 / a) a = - 72 / a \cdot (5 - a) (2 a - 72) a = - 72 \cdot (5 - a) (2 a - 72) a = - 72 \cdot (5 - a) 2 a^{2} - 144 a + 360 = 0 2 . . . prime number 144 = 2^{4} \cdot 3^{2} 360 = 2^{3} \cdot 3^{2} \cdot 5 GCD (2, 144, 360) = 2 a^{2} - 72 a + 180 = 0 p = 1; q = - 72; r = 180 D = q^{2} - 4 p r = 7 2^{2} - 4 \cdot 1 \cdot 180 = 4464 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{7 2 \pm 4 4 6 4}{2} = \frac{7 2 \pm 1 2 3 1}{2} a_{1, 2} = 36 \pm 33.406586 a_{1} = 69.406586177 a_{2} = 2.593413823 b_{1} = 72 / a_{1} = 72 / 69.4066 ≐ 1.0374 b_{2} = 72 / a_{2} = 72 / 2.5934 ≐ 27.7626 k_{1} = - \frac{b _{1}}{a _{1}} = - \frac{1 . 0 3 7 4}{6 9 . 4 0 6 6} = - 0.0149

Our quadratic equation calculator calculates it.

k_{2} = - \frac{b _{2}}{a _{2}} = - \frac{2 7 . 7 6 2 6}{2 . 5 9 3 4} = - 10.7051

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Showing 1 comment:

Math student

this is hard

1 year ago 1 Like Like

Tips for related online calculators

The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Are you looking for help with calculating roots of a quadratic equation?
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
See also our right triangle calculator.
See also our trigonometric triangle calculator.