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• 0 ## Question What is the area of the triangle ABC with A(e,p) B(2e,3p) and C(3e,5p), where p = PI (3.14159265)?

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• 0 point A and B

(x-e)/(y-p)=(e-2e)/(p-3p)

x-e=(e/2p)*y-p....equation of line AB

point A and C

(x-e)/(y-p)=(e-3e)/(p-5p)

x-e=(e/2p)*y-p....equation of line AC

A,B,C are on the same line...so cannot form a triangle...Area(ABC)=0

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• 0 What is the area of the triangle ABC with A(e,p) B(2e,3p) and C(3e,5p), where p = PI (3.14159265)?

In general, given three points of coordinates

A (x1, y1), B (x2, y2), C (x3, y3), the area of the triangle ABC is given by the following exp​ression:

Area (ABC) = (|x1(y2 - y3) + x2(y3 - y1) + x3(y1-y2)|)/2

In this case: x1=e, y1=p; x2=2e, y2=3p; x3=3e, y3=5p. Thus:

Area(ABC) = (|e(3p-5p) + 2e(5p-p) + 3e(p-3p)|)/2 = 0

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