To find the area of triangle ABO, we first need to find the coordinates of points A and B.
To find point A, we set the two functions equal to each other:
sqrt(3x) = -sqrt(3x) + 6
2sqrt(3x) = 6
sqrt(3x) = 3
3x = 9
x = 3
Plugging x=3 back into either function, we get:
y = sqrt(3*3) = sqrt(9) = 3
So, point A is (3,3).
To find point B, we set y = 0 in the second equation:
0 = -sqrt(3x) + 6
sqrt(3x) = 6
3x = 36
x = 12
So, point B is (12,0).
Now, we have the coordinates of points A, B, and O, which is the origin.
The distance between points A and B, AB, is the difference in the x-coordinates:
AB = 12 -3 = 9
The height of the triangle, h, is the y-coordinate of point A, which is 3.
Using the formula for the area of a triangle:
S = 0.5 * base * height
S = 0.5 * 9 * 3
S = 13.5
So, the area of triangle ABO is 13.5 square units.
When lines y=square root of 3x and y=-square root of 3x +6 intersect at point A, and line y=- square root of 3x +6 and the x axis intersect at point B.
Find the area S of triangle ABO
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