Let mathrm{A}(-2,-1), mathrm{B}(1,0), mathrm{ | vedclass

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

Question

$\mathrm{P} \equiv\left(\frac{\alpha-2}{2}, \frac{\beta-1}{2}\right) \equiv\left(\frac{\gamma+1}{2}, \frac{\delta}{2}\right) $

$ \frac{\alpha-2}{2}

Vedclass · Accepted Answer

$32$

Vedclass · Answer

$\mathrm{P} \equiv\left(\frac{\alpha-2}{2}, \frac{\beta-1}{2}ight) \equiv\left(\frac{\gamma+1}{2}, \frac{\delta}{2}ight) $

$ \frac{\alpha-2}{2}=\frac{\gamma+1}{2} 	ext { and } \frac{\beta-1}{2}=\frac{\delta}{2} $

$\Rightarrow \alpha-\gamma=3 \ldots . .(1), \beta-\delta=1 \ldots ....(2)$

Also, $(\gamma, \delta)$ lies on $3 x-2 y=6$

$3 \gamma-2 \delta=6$

and $(\alpha, \beta)$ lies on $2 x-y=5$

$\Rightarrow 2 \alpha-\beta=5 	ext {......(4) }$

Solving $(1), (2), (3), (4)$

$\alpha=-3, \beta=-11, \gamma=-6, \delta=-12$

$|\alpha+\beta+\gamma+\delta|=32$

Let $\mathrm{A}(-2,-1), \mathrm{B}(1,0), \mathrm{C}(\alpha, \beta)$ and $\mathrm{D}(\gamma, \delta)$ be the vertices of a parallelogram $A B C D$. If the point $C$ lies on $2 x-y=5$ and the point $D$ lies on $3 x-2 y=6$, then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to_____.

Similar Questions

The equation of the line which makes right angled triangle with axes whose area is $6$ sq. units and whose hypotenuse is of $5$ units, is

Locus of the points which are at equal distance from $3x + 4y - 11 = 0$ and $12x + 5y + 2 = 0$ and which is near the origin is

Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation to one diagonal is $11x + 7y = 9$, then the equation to the other diagonal is :-

The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$ and the third side passes through the point $(1, -10)$. The equation of the third side is

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in $5\,hr$ and the second one burns in $3\,h$. Both the candles are lit together. After how many minutes the length of the first candle is $3$ times that of the other?