First slide

Equation of line in Straight lines

Question

Two points $(a, 3)$ and $(5, b)$ are the opposite vertices of a rectangle. If the other two vertices lie on the line $y = 2 x + c$ which passes through the point $(a, b)$ then the value of $c$ is

Moderate

A

$- 7$
B

$- 4$
C

0
D

7

Solution

Mid point of the line joining the given points lie on the given line
$\frac{3 + b}{2} = 2 (\frac{a + 5}{2}) + c$
$\Rightarrow 2 a + 2 c - b + 7 = 0$ (i)
Also since the given line passes through $(a, b)$
$b = 2 a + c$ (ii)
Solving (i) and (ii) we get $c = - 7$

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