When lines y=√3x and y =-√3x+6 intersect at point A, and line y=-√3x+6 and the x axis intersect at point B solve the following problems

Question

1)Find the points of intersection A and B.

Answer 1

To find the point of intersection A, we can set the two equations equal to each other:

√3x = -√3x + 6
2√3x = 6
x = 3/√3
x = √3

Now, plug this value of x back into either of the original equations to find the y-coordinate:

y = √3(√3)
y = 3

So, point A is (3, 3).

Next, to find the point of intersection B, we can set y = 0 in the equation y = -√3x + 6:

0 = -√3x + 6
√3x = 6
x = 6/√3
x = 2√3

Therefore, point B is (2√3, 0).