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How to write intersecting lines geometery

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I studied applied mathematics, in which I did both a bachelor's and a master's degree. An intersection of two lines is a point where the graphs of two lines cross each other. Every pair of lines does have an intersection, except if the lines are parallel. This means that the lines move in the same direction. You can check whether two lines are parallel by determining their slope.
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Geometry – fundamental statements (Pre-Algebra, Introducing geometry) – Mathplanet

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. The orthogonal lines to a semicircle meet in the center of the diameter. I'm trying to generalize a similar statement for any curve between two points. Both orthogonal lines on that section will be parallel and so they won't intersect at all.
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Geometry – fundamental statements

That is, the slopes of perpendicular lines are opposite reciprocals. Exception: Horizontal and vertical lines are perpendicular, though you can't multiply their slopes, since the slope of a vertical line is undefined. We can write the equation of a line perpendicular to a given line if we know a point on the line and the equation of the given line.
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Here we will cover a method for finding the point of intersection for two linear functions. That is, we will find the x, y coordinate pair for the point were two lines cross. We will call the first one Line 1, and the second Line 2.
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  1. [MEMRES-18]❿❽
    Akash R.08.06.2021

    some links needs to be updated

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