If O(0,0),A(1,2),and B(3,4) are the vertices | vedclass

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

Question

(D) Let $D$ be the midpoint of $AB$. The coordinates of $D$ are $\left(\frac{1+3}{2}, \frac{2+4}{2}\right) = (2,3)$.The median $OD$ passes through $(0

Vedclass · Accepted Answer

$3x^2+xy-2y^2=0$

Vedclass · Answer

(D) Let $D$ be the midpoint of $AB$. The coordinates of $D$ are $\left(\frac{1+3}{2}, \frac{2+4}{2}\right) = (2,3)$.The median $OD$ passes through $(0,0)$ and $(2,3)$. Its equation is $y = \frac{3}{2}x$,which simplifies to $3x-2y=0$.The slope of line $AB$ is $m_{AB} = \frac{4-2}{3-1} = \frac{2}{2} = 1$.The altitude $OE$ is perpendicular to $AB$,so its slope is $m_{OE} = -\frac{1}{m_{AB}} = -1$.The equation of the altitude $OE$ is $y = -x$,which simplifies to $x+y=0$.The joint equation of the median and altitude is $(3x-2y)(x+y) = 0$.Expanding this,we get $3x^2 + 3xy - 2xy - 2y^2 = 0$,which is $3x^2 + xy - 2y^2 = 0$.

If $O(0,0)$,$A(1,2)$,and $B(3,4)$ are the vertices of triangle $OAB$,then the joint equation of the altitude and median drawn from $O$ is

Similar Questions

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

The product of the lengths of the perpendiculars from the origin to the pair of lines $x^2 + 3y^2 + 4xy - 4x - 10y + 3 = 0$ is

$A$ second degree homogeneous equation in $x$ and $y$ always represents:

If the slopes of the lines given by the equation $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $5:3$,then the ratio $h^{2}:ab$ is:

The area of the triangle formed by the lines $x^2 - 4y^2 = 0$ and $x = a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module