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Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1?
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Understanding the Problem
To find the ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4), we need to use the section formula. The y-axis has the equation x = 0.
Identifying the Points
- Point A: (5, –6)
- Point B: (–1, –4)
Using the Section Formula
The section formula states that if a point P divides the line segment joining points A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, the coordinates of point P can be given as:
\[
P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]
In our case, since the point lies on the y-axis, x-coordinate of P will be 0.
Setting Up the Equation
Let the ratio be m:n. Thus,
\[
0 = \frac{m(-1) + n(5)}{m+n}
\]
This leads to:
\[
m(-1) + n(5) = 0
\]
Which simplifies to:
\[
n(5) = m
\]
This gives us the relationship:
\[
\frac{m}{n} = \frac{5}{1}
\]
Conclusion
Thus, the ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4) is 5:1.
To find the ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4), we need to use the section formula. The y-axis has the equation x = 0.
Identifying the Points
- Point A: (5, –6)
- Point B: (–1, –4)
Using the Section Formula
The section formula states that if a point P divides the line segment joining points A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, the coordinates of point P can be given as:
\[
P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]
In our case, since the point lies on the y-axis, x-coordinate of P will be 0.
Setting Up the Equation
Let the ratio be m:n. Thus,
\[
0 = \frac{m(-1) + n(5)}{m+n}
\]
This leads to:
\[
m(-1) + n(5) = 0
\]
Which simplifies to:
\[
n(5) = m
\]
This gives us the relationship:
\[
\frac{m}{n} = \frac{5}{1}
\]
Conclusion
Thus, the ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4) is 5:1.
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Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1?
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Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1?.
Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.1: Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). 2 points 2:3 5:1 3:5 4:1?.
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