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 \(OBEC\)?

tertre
Mar 12, 2018

#1**+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

CPhill
Mar 12, 2018