The orthocentre of the triangle whose vertice | vedclass

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

Question

(B) Let the vertices be $A(0, 0)$,$B(2, -1)$,and $C(1, 3)$.$1$. Find the equation of altitude from $A$ to $BC$:Slope of $BC = \frac{3 - (-1)}{1 - 2} =

Vedclass · Accepted Answer

$\left( -\frac{4}{7}, -\frac{1}{7} \right)$

Vedclass · Answer

(B) Let the vertices be $A(0, 0)$,$B(2, -1)$,and $C(1, 3)$.$1$. Find the equation of altitude from $A$ to $BC$:Slope of $BC = \frac{3 - (-1)}{1 - 2} = \frac{4}{-1} = -4$.The slope of the altitude $AD$ is the negative reciprocal of the slope of $BC$,which is $\frac{1}{4}$.The equation of $AD$ passing through $A(0, 0)$ is $y - 0 = \frac{1}{4}(x - 0)$,which simplifies to $x - 4y = 0$ ..... $(i)$.$2$. Find the equation of altitude from $B$ to $AC$:Slope of $AC = \frac{3 - 0}{1 - 0} = 3$.The slope of the altitude $BE$ is the negative reciprocal of the slope of $AC$,which is $-\frac{1}{3}$.The equation of $BE$ passing through $B(2, -1)$ is $y - (-1) = -\frac{1}{3}(x - 2)$,which simplifies to $3(y + 1) = -(x - 2)$ $\Rightarrow 3y + 3 = -x + 2$ $\Rightarrow x + 3y + 1 = 0$ ..... $(ii)$.$3$. Solve the system of equations $(i)$ and $(ii)$:From $(i)$,$x = 4y$. Substitute this into $(ii)$:$4y + 3y + 1 = 0$ $\Rightarrow 7y = -1$ $\Rightarrow y = -\frac{1}{7}$.Then $x = 4(-\frac{1}{7}) = -\frac{4}{7}$.Thus,the orthocentre is $\left( -\frac{4}{7}, -\frac{1}{7} \right)$.

The orthocentre of the triangle whose vertices are $(0, 0)$,$(2, -1)$,and $(1, 3)$ is

Similar Questions

$ABC$ is a triangle,$G$ is the centroid,and $D$ is the mid-point of $BC$. If $A = (2, 3)$ and $G = (7, 5)$,then the point $D$ is

The centroid of a triangle,whose vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$,is

If $P(6,1)$ is the orthocentre of the triangle whose vertices are $A(5,-2)$,$B(8,3)$,and $C(h, k)$,then the point $C$ lies on the circle:

If the orthocenter of a triangle is $(1, 1)$ and the circumcenter is $\left( \frac{3}{2}, \frac{3}{4} \right)$,find its centroid.

If a $\triangle ABC$ has vertices $A(-1, 7)$,$B(-7, 1)$ and $C(5, -5)$,then its orthocentre has coordinates

Vedclass Test Series

Exam Paper Generator

Online Exam Module