Question 597115
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Red line:  TO the house 5 for every 8 right:  *[tex \LARGE m\ =\ \frac{-5}{8}]


Using the point-slope form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 9\ =\ -\frac{5}{8}(x\ -\ 0)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{5}{8}x\ +\ 9]


Green line:  AWAY from the house 1 for every 4 right:  *[tex \LARGE m\ =\ \frac{1}{4}]


Using the point-slope form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 2\ =\ \frac{1}{4}(x\ -\ 0)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1}{4}x\ +\ 2]
 

Set the two left-hand sides equal to solve for the *[tex \LARGE x]-coordinate of the point of intersection:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -\frac{5}{8}x\ +\ 9\ =\ \frac{1}{4}x\ +\ 2]


Solve for *[tex \LARGE x] then substitute the value for *[tex \LARGE x] back into either equation to find the *[tex \LARGE y]-coordinate of the point of intersection.  Examine the graph to make sure your answer makes sense.


Use the segment with the endpoints on the *[tex \LARGE y]-axis as the base of the triangle.  The measure of the base will be the difference between the *[tex \LARGE y]-coordinates of the endpoints.  Construct a perpendicular from the base through the point of intersection you calculated above.  The segment from the base to the point of intersection will be the altitude and the measure of the altitude will be the *[tex \LARGE x]-coordinate of the point of intersection.


The area of a triangle is the base times the height divided by 2.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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