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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(9,0) and the y-axis at D. The lines intersect at E(4,4). What is the area of the shaded quadrilateral OBEC?

 

 Apr 21, 2021
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Since  E   is on the  line  containing AB,  the equation of this line is

 

t = -2 (x - 4) + 4

 

y  = -2x +  8 + 4

 

y =  -2x  +  12

 

B = (  0,, -12)     and           0  =  -2x + 12  →   -12 = -2x  ⇒    x = 6   = the x intercept  =  A  = (6,0) 

 

The  shaded  area  is composed of  two  triangles

 

Triangle   EAC   with  a base of 3  and height of 4   ....its  area =  3 * 4 / 2   =  6

 

Triangle  BOA  with a base of 6  and  eight  of 12....its  area  =  6 * 12 / 2  =  36

 

Total shaded area  =   6 + 36  =    42

 

 

cool cool cool

 Apr 21, 2021

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