The coordinates of the orthocenter of the tri | vedclass

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(A) Step $1$: Check the slopes of the lines. Slope of $L_1$ is $m_1 = 4/7$. Slope of $L_3$ is $m_3 = -7/4$. Since $m_1 	imes m_3 = (4/7) 	imes (-7/4

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$(1, 2)$

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(A) Step $1$: Check the slopes of the lines. Slope of $L_1$ is $m_1 = 4/7$. Slope of $L_3$ is $m_3 = -7/4$. Since $m_1 	imes m_3 = (4/7) 	imes (-7/4) = -1$, the lines $L_1$ and $L_3$ are perpendicular.Step $2$: In a right-angled triangle, the orthocenter is the vertex where the right angle is formed.Step $3$: Find the intersection of $L_1$ and $L_3$ by solving the system:$4x - 7y = -10$$7x + 4y = 15$Multiply the first by $4$ and the second by $7$: $16x - 28y = -40$ and $49x + 28y = 105$.Adding them: $65x = 65 \implies x = 1$.Substitute $x=1$ into $x + y = 5$: $1 + y = 5 \implies y = 4$. Wait, checking intersection of $L_1$ and $L_3$: $4(1) - 7y = -10 \implies -7y = -14 \implies y = 2$. The intersection is $(1, 2)$.

The coordinates of the orthocenter of the triangle whose sides are represented by the lines $L_1: 4x - 7y + 10 = 0$, $L_2: x + y - 5 = 0$ and $L_3: 7x + 4y - 15 = 0$ are...

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