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 equation $2x^2 + 4xy - py^2 + 4x + qy + 1 = 0$ will represent two mutually perpendicular straight lines,if

If the pair of lines $6x^2+xy-y^2=0$ and $3x^2-axy-y^2=0$ with $a>0$ have a common line,then $a=$

Find the length of the intercept cut by the pair of lines $2x^2 + 4xy - 4y^2 - 6x - 8y + 7 = 0$ on the $Y$-axis.

If the slope of one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is $\lambda$ times that of the other,then:

If two of the lines represented by $2x^3+x^2y+y^3=0$ are mutually perpendicular,then the slope of the third line is

Vedclass Test Series

Exam Paper Generator

Online Exam Module