The coordinates of the orthocenter of the tri | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$(1, 2)$

Vedclass · Answer

(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 $4x - 7y = -10$: $4(1) - 7y = -10 \implies -7y = -14 \implies y = 2$. 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...

Similar Questions

In the triangle $ABC$ with vertices $A(2, 3)$,$B(4, -1)$ and $C(1, 2)$,find the equation and length of the altitude from the vertex $A$.

The circumcentre of the triangle with vertices $(-2, 3)$,$(2, -1)$,and $(4, 0)$ is:

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

If the coordinates of the vertices of the triangle $ABC$ are $A(-1, 6)$,$B(-3, -9)$,and $C(5, -8)$,then the equation of the median through $C$ is

Find the orthocenter of the triangle with vertices $A(0, 0)$,$B(3, 4)$,and $C(4, 0)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module