The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0

Question

The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0 (A) are concurrent. (B) form a right angled triangle. (C) form an isosceles triangle (D) form an equilateral triangle

Tardigrade Admin · Accepted Answer

Lines II and III are at right angles [ ∵ ((2/3))(- (3/2)) = - 1 Lines I and II intersect at the point (1, 2) and (1, 2) does not belong to III. Hence, the lines are not concurrent, i.e., they form a right angled triangle.

Q. The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0

are concurrent.

form a right angled triangle.

form an isosceles triangle

form an equilateral triangle

Lines II and III are at right angles
$[∵ (\frac{2}{3}) (- \frac{3}{2}) = - 1$
Lines I and II intersect at the point (1, 2) and (1, 2) does not belong to III. Hence, the lines are not concurrent, i.e., they form a right angled triangle.

Q. The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0

are concurrent.

form a right angled triangle.

form an isosceles triangle

form an equilateral triangle

Lines II and III are at right angles [∵(32​)(−23​)=−1 Lines I and II intersect at the point (1, 2) and (1, 2) does not belong to III. Hence, the lines are not concurrent, i.e., they form a right angled triangle.

Lines II and III are at right angles
$[∵ (\frac{2}{3}) (- \frac{3}{2}) = - 1$
Lines I and II intersect at the point (1, 2) and (1, 2) does not belong to III. Hence, the lines are not concurrent, i.e., they form a right angled triangle.