Consider the straight lines L1: x-y = 1 L2: x-y = 1 L3: 2x-2y = 5 L4: 2x-2y = 7 The correct statement is

Question

Consider the straight lines L1: x-y = 1 L2: x-y = 1 L3: 2x-2y = 5 L4: 2x-2y = 7 The correct statement is (A) L1||L4, L2||L3, L1 intersect L4. (B) L1 ⊥ L2, L1||L3, L1 intersect L2. (C) L1 ⊥ L2, L2||L3, L1 intersect L4. (D) L1 ⊥ L2, L1 ⊥ L3, L2 intersect L4.

Tardigrade Admin · Accepted Answer

Consider the lines L1: x-y = 1 L2: x-y = 1 L3: 2x-2y = 5 L4: 2x-2y = 7 L1⊥ L2 is correct statement (∵ Product of their slopes = - 1) L1⊥ L3 is also correct statement (∵ Product of their slopes = - 1) Now, L2: x + y = 1 L4: 2x - 2y = 7 ⇒ 2x-2(1-x) = 7 ⇒ 2x-2 + 2x = 7 ⇒ x = (9/4) and y = (-5/4) Hence, L2 intersects L4.

Q. Consider the straight lines
$L_{1} : x - y = 1$
$L_{2} : x - y = 1$
$L_{3} : 2 x - 2 y = 5$
$L_{4} : 2 x - 2 y = 7$
The correct statement is

$L_{1} ∣ ∣ L_{4}, L_{2} ∣ ∣ L_{3}, L_{1}$ intersect $L_{4} .$

$L_{1} ⊥ L_{2}, L_{1} ∣ ∣ L_{3}, L_{1}$ intersect $L_{2} .$

$L_{1} ⊥ L_{2}, L_{2} ∣ ∣ L_{3}, L_{1}$ intersect $L_{4} .$

$L_{1} ⊥ L_{2}, L_{1} ⊥ L_{3}, L_{2}$ intersect $L_{4} .$

Q. Consider the straight lines L1​:x−y=1 L2​:x−y=1 L3​:2x−2y=5 L4​:2x−2y=7 The correct statement is

L1​∣∣L4​,L2​∣∣L3​,L1​ intersect L4​.

L1​⊥L2​,L1​∣∣L3​,L1​ intersect L2​.

L1​⊥L2​,L2​∣∣L3​,L1​ intersect L4​.

L1​⊥L2​,L1​⊥L3​,L2​ intersect L4​.

Q. Consider the straight lines
$L_{1} : x - y = 1$
$L_{2} : x - y = 1$
$L_{3} : 2 x - 2 y = 5$
$L_{4} : 2 x - 2 y = 7$
The correct statement is

$L_{1} ∣ ∣ L_{4}, L_{2} ∣ ∣ L_{3}, L_{1}$ intersect $L_{4} .$

$L_{1} ⊥ L_{2}, L_{1} ∣ ∣ L_{3}, L_{1}$ intersect $L_{2} .$

$L_{1} ⊥ L_{2}, L_{2} ∣ ∣ L_{3}, L_{1}$ intersect $L_{4} .$

$L_{1} ⊥ L_{2}, L_{1} ⊥ L_{3}, L_{2}$ intersect $L_{4} .$