JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q78

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MathematicsSingle correct+4 / -1Question 78 of 90

Two sides of a rhombus are along the lines, $x-y+1=0$ and $7x-y-5=0$ . If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus ?

(−3, −9)

(−3, −8)

\left(\dfrac13,-\dfrac83\right)

\left(-\dfrac{10}3,-\dfrac73\right)

Answer and worked solution

Official answer: C

The given sides meet at the vertex (1, 2), so the opposite vertex is (−3, −6). The side through it parallel to $x-y+1=0$ is $x-y-3=0$ ; it meets $7x-y-5=0$ at $\left(\frac13,-\frac83\right)$ , which is a vertex.

Topics:Equations of a line

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 78