The orthocentre of the triangle formed by the | vedclass

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

Question

(D) Let the vertices of the triangle be $A(1,3), B(-3,5)$,and $C(5,-1)$.Slope of $AC = \frac{-1-3}{5-1} = \frac{-4}{4} = -1$.The altitude from $B$ to

Vedclass · Accepted Answer

$(19,27)$

Vedclass · Answer

(D) Let the vertices of the triangle be $A(1,3), B(-3,5)$,and $C(5,-1)$.Slope of $AC = \frac{-1-3}{5-1} = \frac{-4}{4} = -1$.The altitude from $B$ to $AC$ is perpendicular to $AC$. Let its slope be $m_1$. Since $m_1 	imes (-1) = -1$,$m_1 = 1$.The equation of the altitude from $B(-3,5)$ is $(y-5) = 1(x+3) \Rightarrow x-y = -8$ (Equation $i$).Slope of $BC = \frac{-1-5}{5-(-3)} = \frac{-6}{8} = -\frac{3}{4}$.The altitude from $A$ to $BC$ is perpendicular to $BC$. Let its slope be $m_2$. Since $m_2 	imes (-\frac{3}{4}) = -1$,$m_2 = \frac{4}{3}$.The equation of the altitude from $A(1,3)$ is $(y-3) = \frac{4}{3}(x-1)$ $\Rightarrow 3y-9 = 4x-4$ $\Rightarrow 4x-3y = -5$ (Equation $ii$).To find the orthocentre,solve the system of equations:$x-y = -8 \Rightarrow 3x-3y = -24$ (Equation $iii$).Subtracting (ii) from (iii): $(3x-3y) - (4x-3y) = -24 - (-5)$ $\Rightarrow -x = -19$ $\Rightarrow x = 19$.Substituting $x=19$ into $(i)$: $19-y = -8 \Rightarrow y = 27$.Thus,the orthocentre is $(19,27)$.

The orthocentre of the triangle formed by the points $(1,3), (-3,5)$ and $(5,-1)$ is

Similar Questions

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

If $\left( \frac{3}{2}, 0 \right)$,$\left( \frac{3}{2}, 6 \right)$,and $(-1, 6)$ are the midpoints of the sides of a triangle,find the incenter of the triangle.

What is the distance of the orthocenter from the vertex of a triangle with vertices $(2, 3), (4, 5),$ and $(-1, 10)$?

If the vertices of a triangle are $A(1, 4)$,$B(3, 0)$,and $C(2, 1)$,then the length of the median passing through $C$ is

Let $A(-3, 2)$ and $B(-2, 1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y + 2 = 0$,then the vertex $C$ lies on the line

Vedclass Test Series

Exam Paper Generator

Online Exam Module