Math Problem Statement
Find the ratio in which y-axis divides the line segment joining the points A(5, -6) and
B (-1, -4). Also find the coordinates of the point of division.
Solution
To find the ratio in which the y-axis divides the line segment joining the points and , and to find the coordinates of the point of division, we can use the section formula.
The section formula states that the coordinates of a point dividing the line segment joining points and in the ratio are given by:
Since the y-axis divides the segment, the x-coordinate of the point of division is . Let's denote the ratio in which the y-axis divides the segment by . Then, using the section formula for the x-coordinate, we have:
Simplify and solve for :
Multiplying both sides by :
Thus,
So, the y-axis divides the line segment in the ratio .
Now, let's find the coordinates of the point of division. Using the section formula for the y-coordinate:
Therefore, the coordinates of the point of division are:
In summary:
- The ratio in which the y-axis divides the line segment joining the points and is .
- The coordinates of the point of division are .
Would you like further details or have any questions?
Here are 8 related questions to explore further:
- How does the section formula change if the ratio is given as a fraction instead of an integer?
- Can you verify the ratio by considering the distances from the y-axis?
- What happens if the dividing line is not the y-axis but a different vertical line?
- How do you find the coordinates of the point dividing a segment in a given ratio on the x-axis?
- What are the applications of the section formula in real-life scenarios?
- How do you find the coordinates of a point dividing a segment in a given ratio in 3D space?
- Can you derive the section formula from the basic principles of coordinate geometry?
- How do you solve similar problems where the dividing point lies on a line other than the coordinate axes?
Tip: When working with ratios in coordinate geometry, always make sure to express the ratio clearly and verify your results by substituting back into the original formula or context.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Ratio Division
Formulas
Section formula for dividing a line segment
Theorems
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Suitable Grade Level
Grades 9-12
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