Two sides of a parallelogram are along the li | vedclass

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

Question

(C) Let the parallelogram be $ABCD$. The lines $4x + 5y = 0$ and $7x + 2y = 0$ intersect at the origin $A(0, 0)$.Let the diagonal $BD$ lie on the line

Vedclass · Accepted Answer

$(2, 2)$

Vedclass · Answer

(C) Let the parallelogram be $ABCD$. The lines $4x + 5y = 0$ and $7x + 2y = 0$ intersect at the origin $A(0, 0)$.Let the diagonal $BD$ lie on the line $11x + 7y = 9$.Point $D$ is the intersection of $4x + 5y = 0$ and $11x + 7y = 9$. Solving these,we get $D = (5/3, -4/3)$.Point $B$ is the intersection of $7x + 2y = 0$ and $11x + 7y = 9$. Solving these,we get $B = (-2/3, 7/3)$.The diagonals of a parallelogram bisect each other. Let $M$ be the midpoint of $BD$.$M = (\frac{5/3 - 2/3}{2}, \frac{-4/3 + 7/3}{2}) = (1/2, 1/2)$.The other diagonal $AC$ passes through $A(0, 0)$ and $M(1/2, 1/2)$.The equation of line $AC$ is $y - 0 = \frac{1/2 - 0}{1/2 - 0}(x - 0)$,which simplifies to $y = x$.Checking the options,the point $(2, 2)$ satisfies $y = x$.

Two sides of a parallelogram are along the lines $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one of the diagonals of the parallelogram is $11x + 7y = 9$,then the other diagonal passes through the point:

Similar Questions

Three vertices of a triangle are $A(4, 3)$,$B(1, -1)$,and $C(7, k)$. The value$(s)$ of $k$ for which the centroid,orthocentre,incentre,and circumcentre of the $\Delta ABC$ lie on the same straight line is/are:

Let the equations of two adjacent sides of a parallelogram $ABCD$ be $2x - 3y = -23$ and $5x + 4y = 23$. If the equation of its one diagonal $AC$ is $3x + 7y = 23$ and the distance of $A$ from the other diagonal is $d$,then $50d^2$ is equal to $........$.

The set of values that $\beta$ can assume so that the point $(0, \beta)$ lies on or inside the triangle formed by the lines $3x+y+2=0$,$2x-3y+5=0$,and $x+4y-14=0$ is

The sides of a $\triangle ABC$ are positive integers. The smallest side has length $1$. Which of the following statements is true?

Let $A(h, k)$,$B(1, 1)$,and $C(2, 1)$ be the vertices of a right-angled triangle with $AC$ as the hypotenuse. If the area of the triangle is $1$,then which of the following can be the set of values for $k$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module