How to find last point of this triangle triangle?

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How to find last point of this triangle triangle?

I got $(1,7)$ and $(0.5, 4)$. The equations are $y = 3|2x − 1| + 4$ and $y = −|x − 4| + 10$

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solve y=-6x+7 (x< 1/2), and y=x+6(x<4). You will get (1/7, 43/7)