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A line with slope of -2 intersects the positive x-axis at A and the positive y-axis at B. A second line intersects the x-axis at \(C(8,0)\) and the y-axis at D. The lines intersect at \(E(4,4)\). What is the area of the shaded quadrilateral  \(OBEC\)?

 

 Mar 12, 2018
 #1
avatar+101746 
+1

The equation of BA  is

 

y = -2 (x - 4) + 4

y = -2x + 8 + 4

y   = -2x + 12

 

So..."B"  =  -2(0) + 12  =  12

 

And "A"  can be found as

0  = -2x + 12

2x  = 12

x = 6

So..."A"  =  (6,0)

 

So.....the area of the shaded quadrilateral   =  

 

Area of triangle OBA  +  area of triangle EAC  =

{Note that EAC has a base of 2  and a height of 4 }

 

(1/2)(12*6)  + (1/2)(4*2)    =

 

36 + 4   =

 

40 units^2 

 

 

 

cool cool cool

 Mar 12, 2018
 #2
avatar+4295 
+1

Thanks so much, CPhill! Great job!

tertre  Mar 13, 2018

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