Points (1, 3) and (5, 1) are opposite vertices of a rectangle. other two vertices lie on line y = 2x

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9.Straight Line

easy

The points $(1, 3)$ and $(5, 1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c,$ then the value of c will be

$4$

$-4$

$2$

$-2$

(IIT-1981)

Solution

(b) Let $ABCD$ be a rectangle. Given $A\, (1, 3)$ and $C\, (5, 1)$. Equation $B$ and $D$ lie on $y = 2x + c$

We know that intersecting point of diagonal of rectangle is same or at midpoint. So mid point of $AC$ is $(3, 2)$. So $y = 2x + c$ passes throguh $(3, 2)$. Hence $c = – 4$.

Standard 11

Mathematics

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The points $(1, 3)$ and $(5, 1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c,$ then the value of c will be

Solution

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