First slide

Equation of line in Straight lines

Question

$Two sides of a parallelogram are along the lines x + y = 3 and x - y + 3 = 0 . If its$
$diagonals intersect at (2, 4) then one of its vertex is$

Moderate

A

$(3, 5)$
B

$(2, 1)$
C

$(2, 6)$
D

$(3, 6)$

Solution

solving the given equations A(0,3) and $P (2, 4)$ is the midpoint
using midpoint formula we get C(4,5)
given lines are perpendicular hence the figure formed is a rectangle
let the equation of BC be x-y+k=0 sub C we get k=1
let the equation of CD be x+y+c=0 sub C we get c=-9
solving BC and AB we get B(1,2)
solving CD and AD we get D(3,6)

$D (3, 6)$

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