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Solution

Vertices: $A(0,0),\ B(4,0),\ C(3,4)$ Slope of $BC = \dfrac{4 - 0}{3 - 4} = -4$ Equation of altitude from $A$: perpendicular to BC → slope $\dfrac{1}{4}$ $\Rightarrow y = \dfrac{1}{4}x$ … (1) Slope of $AC = \dfrac{4 - 0}{3 - 0} = \dfrac{4}{3}$ Equation of altitude from $B$: perpendicular slope $-\dfrac{3}{4}$, passes through $(4,0)$ $\Rightarrow y - 0 = -\dfrac{3}{4}(x - 4)$ $\Rightarrow y = -\dfrac{3}{4}x + 3$ … (2) Solving (1) and (2): $\dfrac{x}{4} = -\dfrac{3x}{4} + 3 \Rightarrow x = 3,\ y = \dfrac{3}{4}$