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Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis?
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Two perpendicular lines intersect at the point with coordinates (6,5)....
Intersection of Perpendicular Lines
Given: Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin.
Finding the Intersection with the X-axis
- Equation of the line passing through the origin: Since one of the lines passes through the origin, its equation can be written in the form y = mx. Given that it passes through (6,5), we can substitute these coordinates into the equation to find the slope m.
- Equation of the perpendicular line: The slope of the perpendicular line will be the negative reciprocal of the slope of the line passing through the origin. Let this line intersect the x-axis at point (a,0).
- Finding the equation of the perpendicular line: Using the slope we found earlier, we can write the equation of the perpendicular line in the form y = mx + b and substitute the coordinates of the point of intersection (6,5) to solve for b.
- Finding the x-intercept: Once we have the equation of the perpendicular line (y = mx + b), we can set y = 0 and solve for x to find the x-coordinate of the point where the line intersects the x-axis.
By following these steps, you can determine where the perpendicular line intersects the x-axis in relation to the given point of intersection at (6,5). This method allows you to find the solution analytically and understand the geometric relationship between the two perpendicular lines.
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Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis?
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Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis?.
Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two perpendicular lines intersect at the point with coordinates (6,5). One line passes through the origin. Where does the other line intersect the x-axis?.
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