First slide

Equation of line in Straight lines

Question

Given four lines whose equations are $x + 2 y -$ $3 = 0, 2 x + 3 y - 4 = 0, 3 x + 4 y - 7 = 0$ and $4 x + 5 y - 6 = 0$ , then the lines are

Moderate

A

concurrent
B

the sides of a quadrilateral with one vertex at (3, 0)
C

the sides of a cyclic quadrilateral
D

none of these

Solution

Three lines $x + 2 y - 3 = 0, 2 x + 3 y - 4 = 0$ and
$4 x + 5 y - 6 = 0$ are concurrent at $(- 1, 2) .$ But the
fourth line $3 x + 4 y - 7 = 0$ does not pass through
this point.

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