+4622 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 \(OBEC\)?
+129899 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
