Let alpha, beta, gamma, delta in mathbb{Z} an | vedclass

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

Question

(D) In a parallelogram,the diagonals bisect each other. Therefore,the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.The midpo

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) In a parallelogram,the diagonals bisect each other. Therefore,the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.The midpoint of $BD$ is $\left(\frac{1+1}{2}, \frac{2+0}{2}\right) = (1, 1)$.The midpoint of $AC$ is $\left(\frac{\alpha+\gamma}{2}, \frac{\beta+\delta}{2}\right)$.Equating the midpoints,we get:$\frac{\alpha+\gamma}{2} = 1 \implies \alpha + \gamma = 2$$\frac{\beta+\delta}{2} = 1 \implies \beta + \delta = 2$We need to find the value of $2(\alpha + \beta + \gamma + \delta)$.Substituting the sums:$2(\alpha + \gamma + \beta + \delta) = 2(2 + 2) = 2(4) = 8$.

Let $\alpha, \beta, \gamma, \delta \in \mathbb{Z}$ and let $A(\alpha, \beta), B(1, 0), C(\gamma, \delta)$ and $D(1, 2)$ be the vertices of a parallelogram $ABCD$. If $AB = \sqrt{10}$ and the points $A$ and $C$ lie on the line $3y = 2x + 1$,then $2(\alpha + \beta + \gamma + \delta)$ is equal to

Similar Questions

The equation of one side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is

The vertices of a triangle are $(2, 1)$,$(5, 2)$ and $(4, 4)$. The lengths of the perpendiculars from these vertices to the opposite sides are

Suppose $ABCD$ is a trapezium whose sides and height are integers and $AB$ is parallel to $CD$. If the area of $ABCD$ is $12$ and the sides are distinct,then $|AB-CD|$ is:

Three points are $A(6, 3)$,$B(-3, 5)$,and $C(4, -2)$. If $P(x, y)$ is a point,then the ratio of the area of $\Delta PBC$ to the area of $\Delta ABC$ is:

The equations of sides $AB$,$BC$,and $CA$ of a $\triangle ABC$ are $2x+y=0$,$x+py=q$,and $x-y=3$ respectively. If $P(2,3)$ is its orthocenter,then the value of $p+q$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module