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# Coordinates

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The line x = k bisects the area of triangle ABC.  Find the value of k.

Apr 19, 2022

#1
+115
-4

let me know if you need any thing else have a great day

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Apr 19, 2022
edited by Kakashi  Apr 19, 2022
#2
+2455
+1

The line $$x = k$$ is a vertical line. It will split the triangle into a right triangle and a quadrilateral.

The area of the triangle is $$10.5$$

The equation of line $$AB$$ is $${3 \over10}x+{9 \over5}$$

We want the area of the right triangle to be $$5.25$$, so we can write the area as an equation: $$10.5=(x+6)({3 \over 10}x+{9 \over 5})$$

Solving the equation and simplifying, we find that $$\color{brown}\boxed{x = \sqrt{35} - 6}$$

Feel free to ask me if you have any questions!!

Apr 19, 2022