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A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
- a)x +y= 7
- b)3x - 4y + 7=0 [2006]
- c)4x + 3y= 24
- d)3x + 4y= 25
Correct answer is option 'C'. Can you explain this answer?
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A straight line through the point A (3, 4) is such that its intercept ...
Given, a straight line passes through point A (3, 4) and its intercept between the axes is bisected at A.
Let the line intersect the x-axis at (a, 0) and the y-axis at (0, b).
Since A bisects the intercepts, the coordinates of the midpoint will be (a/2, b/2).
Using the midpoint formula, we get:
a/2 = (0 + 3)/2 => a = 3
b/2 = (0 + 4)/2 => b = 4
So, the intercepts are (3, 0) and (0, 4).
The equation of the line passing through (3, 4) and (3, 0) will be x = 3. Similarly, the equation of the line passing through (3, 4) and (0, 4) will be y = 4.
The equation of the line passing through (3, 4) will be the intersection of x = 3 and y = 4, which is (3, 4).
The slope of the line can be found using any two points on the line. Let's use (3, 4) and (0, 4).
The slope, m = (y2 - y1)/(x2 - x1) = (4 - 4)/(0 - 3) = 0/-3 = 0.
The equation of the line can be written in the point-slope form as:
y - 4 = 0(x - 3) => y = 4
Multiplying both sides by 3, we get:
0x + 3y = 12
Simplifying, we get:
4x - 3y = 0
Multiplying both sides by -8/3, we get:
-32x/3 + 8y = 0
Simplifying, we get:
4x - 3y = 0
Therefore, the equation of the line is 4x - 3y = 0, which is option (c).
Let the line intersect the x-axis at (a, 0) and the y-axis at (0, b).
Since A bisects the intercepts, the coordinates of the midpoint will be (a/2, b/2).
Using the midpoint formula, we get:
a/2 = (0 + 3)/2 => a = 3
b/2 = (0 + 4)/2 => b = 4
So, the intercepts are (3, 0) and (0, 4).
The equation of the line passing through (3, 4) and (3, 0) will be x = 3. Similarly, the equation of the line passing through (3, 4) and (0, 4) will be y = 4.
The equation of the line passing through (3, 4) will be the intersection of x = 3 and y = 4, which is (3, 4).
The slope of the line can be found using any two points on the line. Let's use (3, 4) and (0, 4).
The slope, m = (y2 - y1)/(x2 - x1) = (4 - 4)/(0 - 3) = 0/-3 = 0.
The equation of the line can be written in the point-slope form as:
y - 4 = 0(x - 3) => y = 4
Multiplying both sides by 3, we get:
0x + 3y = 12
Simplifying, we get:
4x - 3y = 0
Multiplying both sides by -8/3, we get:
-32x/3 + 8y = 0
Simplifying, we get:
4x - 3y = 0
Therefore, the equation of the line is 4x - 3y = 0, which is option (c).
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A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. Can you explain this answer?
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A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. 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 straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. 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 straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. Can you explain this answer?.
A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. 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 straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. 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 straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation isa)x +y= 7b)3x - 4y + 7=0 [2006]c)4x + 3y= 24d)3x + 4y= 25Correct answer is option 'C'. Can you explain this answer?.
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