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 = 2ab ab = 2 36 = 72  k = 5a2b = ab  (2b) a = b   (5a) (272/a) a = 72/a   (5a)  (2a72)a=72 (5a)  (2a72)a=72 (5a) 2a2144a+360=0 2 ...  prime number 144=2432 360=23325 GCD(2,144,360)=2  a272a+180=0  p=1;q=72;r=180 D=q24pr=72241180=4464 D>0  a1,2=2pq±D=272±4464=272±1231 a1,2=36±33.406586 a1=69.406586177 a2=2.593413823  b1=72/a1=72/69.40661.0374 b2=72/a2=72/2.593427.7626 k1=a1b1=69.40661.0374=0.0149

Our quadratic equation calculator calculates it.


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Showing 1 comment:
Math student
this is hard

6 months ago  1 Like

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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.
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