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A triangle is formed by the lines 2x – 3y – 6 = 0 ; 3x – y + 3 = 0 and 3x + 4y – 12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, then
- a)a ∈ [–1, 2] & b ∈ [–2, 3]
- b)a ∈ [–1, 3] & b ∈ [–2, 4]
- c)a ∈ [–2, 4] & b ∈ [–3, 4]
- d)a ∈ [–1, 3] & b ∈ [–2, 3]
Correct answer is option 'D'. Can you explain this answer?
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A triangle is formed by the lines 2x –3y –6 = 0 ; 3x &ndas...
To find the coordinates of the vertices of the triangle, we need to find the points where the lines intersect.
First, let's find the intersection of the lines 2x + 3y = 6 and x - 2y = 4:
2x + 3y = 6
x - 2y = 4
Multiplying the second equation by 2, we get:
2x - 4y = 8
Adding this to the first equation, we eliminate x and get:
-y = 14
So, y = -14.
Substituting this back into the second equation, we get:
x - 2(-14) = 4
x + 28 = 4
x = -24
Therefore, the first vertex of the triangle is (-24, -14).
Next, let's find the intersection of the lines 2x + 3y = 6 and x + 4y = 8:
2x + 3y = 6
x + 4y = 8
Multiplying the first equation by 4 and subtracting the second equation, we get:
5y = -10
So, y = -2.
Substituting this back into the second equation, we get:
x + 4(-2) = 8
x = 16
Therefore, the second vertex of the triangle is (16, -2).
Finally, let's find the intersection of the lines x - 2y = 4 and x + 4y = 8:
x - 2y = 4
x + 4y = 8
Subtracting the first equation from the second, we get:
6y = 4
So, y = 2/3.
Substituting this back into the first equation, we get:
x - 2(2/3) = 4
x = 10/3
Therefore, the third vertex of the triangle is (10/3, 2/3).
To summarize, the vertices of the triangle are (-24, -14), (16, -2), and (10/3, 2/3).
First, let's find the intersection of the lines 2x + 3y = 6 and x - 2y = 4:
2x + 3y = 6
x - 2y = 4
Multiplying the second equation by 2, we get:
2x - 4y = 8
Adding this to the first equation, we eliminate x and get:
-y = 14
So, y = -14.
Substituting this back into the second equation, we get:
x - 2(-14) = 4
x + 28 = 4
x = -24
Therefore, the first vertex of the triangle is (-24, -14).
Next, let's find the intersection of the lines 2x + 3y = 6 and x + 4y = 8:
2x + 3y = 6
x + 4y = 8
Multiplying the first equation by 4 and subtracting the second equation, we get:
5y = -10
So, y = -2.
Substituting this back into the second equation, we get:
x + 4(-2) = 8
x = 16
Therefore, the second vertex of the triangle is (16, -2).
Finally, let's find the intersection of the lines x - 2y = 4 and x + 4y = 8:
x - 2y = 4
x + 4y = 8
Subtracting the first equation from the second, we get:
6y = 4
So, y = 2/3.
Substituting this back into the first equation, we get:
x - 2(2/3) = 4
x = 10/3
Therefore, the third vertex of the triangle is (10/3, 2/3).
To summarize, the vertices of the triangle are (-24, -14), (16, -2), and (10/3, 2/3).
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A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer?
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A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer?.
A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer?.
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A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A triangle is formed by the lines 2x –3y –6 = 0 ; 3x –y + 3 = 0 and 3x + 4y –12 = 0. If the points P(a, 0) and Q(0, b) always lie on or inside the DABC, thena)a ∈ [–1, 2] & b ∈ [–2, 3]b)a ∈ [–1, 3] & b ∈ [–2, 4]c)a ∈ [–2, 4] & b ∈ [–3, 4]d)a ∈ [–1, 3] & b ∈ [–2, 3]Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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