In the , the points with coordinates and lie on line . Line contains the point with coordinates and is perpendicular to line . What is the of the point where lines and intersect?
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It is often helpful to make a sketch for this type of question.
The slope of line is equal to .
Since is the , the equation of is .
Since line is perpendicular to line , the slope of is equal to (the negative reciprocal of the slope of ). Since line contains the point with coordinates, the equation of line can be found by substitution.
To find the of the point where the two lines intersect, solve the equation . The lines intersect at the point where .
It is also possible to graph the two linear equations to determine where they intersect. Using a graphing calculator, let and . You can find the point of intersection graphically in the standard viewing window, or you can examine a table of values to find the where .