The line y = (x-3)/2 intersects the circle x^2 + y^2 at A and B. Find the coordinates of the midpoint of AB.
This is real urgent thank you
+9673 Sorry, but the circle equation is not complete. It should be x^2 + y^2 = (missing part). What is that missing part?
+9673 First, you substitute y = (x - 3)/2 into x^2 + y^2 = 5.
You will get \(x^2 + \left(\dfrac{x - 3}2\right)^2 = 5\)
Now upon simplification, \(5x^2 - 6x - 11 = 0\).
Notice that the solutions to this equation is the x-coordinates of A and x-coordinates of B respectively.
We conclude that the x-coordinate of the midpoint of AB is the sum of roots divided by 2, which is \(\dfrac35\).
By a similar approach, you can find that the y-coordinate of the midpoint is \(-\dfrac65\), which means your answer is correct.
