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

If one of the lines represented by $ax^2+2hxy+by^2=0$ is perpendicular to $mx+ny=18$,then

The product of the perpendicular distances from the origin to the pair of straight lines $12x^2 + 25xy + 12y^2 + 10x + 11y + 2 = 0$ is

If the slope of one of the lines represented by $ax^2 + (2a + 1)xy + 2y^2 = 0$ is the reciprocal of the slope of the other,then the sum of the squares of the slopes is

If $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ represents a pair of lines,which of the following statements is true?

If the equation $\lambda x^{2} + 2y^{2} - 5xy + 5x - 7y + 3 = 0$ represents a pair of straight lines,then $\lambda = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module