Asked by Solta
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (3,2). write the length L of hypotenuse as a function of x.
Answers
Answered by
Reiny
Let the x-intercept of the line be (x,0)
let the y-intercept of the line be (0,y)
we have similar triangles, and by ratios ...
y/x = 3/(x-2)
xy - 2y = 3x
y(x-2) = 3x
y = 3x/(x-2)
L^2 = x^2 + y^2
= x^2 + [3x/(x-2)]^2
= x^2 + 9x^2/(x^2 - 4x + 4)
let the y-intercept of the line be (0,y)
we have similar triangles, and by ratios ...
y/x = 3/(x-2)
xy - 2y = 3x
y(x-2) = 3x
y = 3x/(x-2)
L^2 = x^2 + y^2
= x^2 + [3x/(x-2)]^2
= x^2 + 9x^2/(x^2 - 4x + 4)
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