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

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Showing 1 comment:

Math student

this is hard

6 months ago 1 Like Like

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