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?
+128408 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
