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The equation of the line which passes through the point (1 , - 2) and cuts off equal intercepts from the axis is
- a)x + y + 1 = 0
- b)x + y = 1
- c)x – y – 2 = 0
- d)x – y - 1 = 0
Correct answer is option 'A'. Can you explain this answer?
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The equation of the line which passes through the point (1 , - 2) and ...
Understanding Equal Intercepts
To find the equation of a line that cuts off equal intercepts from the axes, we start with the general form of such a line:
- The equation can be expressed as:
**x + y = c**,
where **c** is the length of the intercepts, meaning the line cuts off intercepts of length **c** on both the x-axis and y-axis.
Finding the Required Equation
1. **Intercepts of the Line**:
The intercepts are at points (c, 0) and (0, c).
2. **Point on the Line**:
We know the line passes through the point (1, -2). Substituting this point into the equation:
**1 + (-2) = c**
This simplifies to:
**c = -1**.
3. **Substituting c in the Equation**:
Since we have found **c = -1**, we can write the equation of the line:
**x + y = -1**.
4. **Rearranging the Equation**:
Rearranging gives us:
**x + y + 1 = 0**.
Conclusion
Thus, the equation of the line that passes through the point (1, -2) and cuts off equal intercepts from the axes is:
**x + y + 1 = 0**.
The correct answer is option 'A'.
To find the equation of a line that cuts off equal intercepts from the axes, we start with the general form of such a line:
- The equation can be expressed as:
**x + y = c**,
where **c** is the length of the intercepts, meaning the line cuts off intercepts of length **c** on both the x-axis and y-axis.
Finding the Required Equation
1. **Intercepts of the Line**:
The intercepts are at points (c, 0) and (0, c).
2. **Point on the Line**:
We know the line passes through the point (1, -2). Substituting this point into the equation:
**1 + (-2) = c**
This simplifies to:
**c = -1**.
3. **Substituting c in the Equation**:
Since we have found **c = -1**, we can write the equation of the line:
**x + y = -1**.
4. **Rearranging the Equation**:
Rearranging gives us:
**x + y + 1 = 0**.
Conclusion
Thus, the equation of the line that passes through the point (1, -2) and cuts off equal intercepts from the axes is:
**x + y + 1 = 0**.
The correct answer is option 'A'.
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The equation of the line which passes through the point (1 , - 2) and cuts off equal intercepts from the axis isa)x + y + 1 = 0b)x + y = 1c)x – y – 2 = 0d)x – y - 1 = 0Correct answer is option 'A'. Can you explain this answer?
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The equation of the line which passes through the point (1 , - 2) and cuts off equal intercepts from the axis isa)x + y + 1 = 0b)x + y = 1c)x – y – 2 = 0d)x – y - 1 = 0Correct answer is option 'A'. 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 The equation of the line which passes through the point (1 , - 2) and cuts off equal intercepts from the axis isa)x + y + 1 = 0b)x + y = 1c)x – y – 2 = 0d)x – y - 1 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the line which passes through the point (1 , - 2) and cuts off equal intercepts from the axis isa)x + y + 1 = 0b)x + y = 1c)x – y – 2 = 0d)x – y - 1 = 0Correct answer is option 'A'. Can you explain this answer?.
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