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
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
- [IIT 1984]
- A
$y = \sqrt 3 x + 9$ but not $y = -\sqrt 3 x + 9$
- B
$3x + y + 7 = 0$ but not $3x + y - 7 = 0$
- C
$3x + y + 7 = 0$ or $x - 3y - 31 = 0$
- D
Neither $3x + y + 7$ nor $x - 3y - 31 = 0$
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Let $\alpha, \beta, \gamma, \delta \in \mathrm{Z}$ and let $\mathrm{A}(\alpha, \beta), \mathrm{B}(1,0), \mathrm{C}(\gamma, \delta)$ and $D(1,2)$ be the vertices of a parallelogram $\mathrm{ABCD}$. If $\mathrm{AB}=\sqrt{10}$ and the points $\mathrm{A}$ and $\mathrm{C}$ lie on the line $3 y=2 x+1$, then $2(\alpha+\beta+\gamma+\delta)$ is equal to
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- [JEE MAIN 2024]
Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4,5),(0,7) (5,-5)$ and $(-4,-2) .$ Also, find its area.
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The triangle formed by ${x^2} - 9{y^2} = 0$ and $x = 4$ is
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