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I need to find the point of intersection of a line but they don't match, Am I doing anything wrong or they just don't match, can you help me? the coordinates are

$A(2,-3)$, $B(0,-2)$.

$A(2,-9)$, $B(0,-8)$.

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    Please do add what you have already tried, so we can either see your mistake or give you a hint on how to solve it. – 2017-01-29
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    The points of intersection of what? The two lines determined by the two pairs of points? – 2017-01-29
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    @Gab Hi. What you are asking is a bit unclear. I've written an answer which refers to the two straight lines connecting the two pairs of points. If this is not what you are looking for, please tell us, so that we can provide better answers. – 2017-01-29
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    they are two lines, apparently you have to find the equation, solve them, find x and y for both lines and check the intersection. i have deleted my notes already. – 2017-01-29
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    Delete this question, get the clarity you intended and re-post it. – 2017-02-11

1 Answers 1

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If you are referring to the straight lines connecting the points, you will see that they indeed do not intersect since they are parallel.

The slope is given by: $$m=\frac{y_2-y_1}{x_2-x_1}$$ For your first line: $$m_1=\frac{-2-(-3)}{0-2}=-\frac{1}{2}$$ For the second line: $$m_2=\frac{-8-(-9)}{0-2}=-\frac{1}{2}$$ $m_1=m_2$, and the lines do not overlap each other. Therefore, there is no point of intersection.

Hope this answers your question.

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    What about A (2,-3) B (0,-2) A (2,2) B (1,0), how do i know if there is intersection with the slope? – 2017-01-29
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    Well, here the intersection certainly exists assuming the lines extend infinitely since $m_1\neq m_2$: $m_1=-\frac{1}{2}$ and $m_2=2$. If you want to find out if the line intersecting is within the two points $A$ and $B$, find an equation for each line and then find the point of intersection using algebra. The point of intersection found should be enough to deduce if it is within the two points. – 2017-01-29