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, solve the following problems. Find the points of intersection A and B

Answer 1

To find the point of intersection A between the lines y = sqrt(3x) and y = -sqrt(3x) + 6, set the two equations equal to each other and solve for x:

sqrt(3x) = -sqrt(3x) + 6
2sqrt(3x) = 6
sqrt(3x) = 3
3x = 9
x = 3

Now, substitute x = 3 into either of the original equations to find the y-coordinate of point A:

y = sqrt(3*3) = sqrt(9) = 3

Therefore, point A is at (3,3).

To find the point of intersection B between the line y = -sqrt(3x) + 6 and the x-axis, set y = 0:

0 = -sqrt(3x) + 6
sqrt(3x) = 6
3x = 36
x = 12

Therefore, point B is at (12,0).