Let A(1,2), B(6,1) and C(7,8) be three points in the plane. Find the equation of the line passing through point C and through the midpoint of the line segment AB. Write answer in the form
ax + by + c = 0.
I found slope of AB to be (-1/5).
I also found the midpoint of AB to be (7/2, 3/2).
I then decided, for unknown reasons, to calculate the slope of the perpendicular bisector to be 5.
I then plugged 5 and the midpoint into point-slope formula and got the wrong answer. Trying a second time through guessing, I decided to plug 5 and point C into the point-slope formula and again got the wrong answer. The textbook does not give a sample representing the question above or else I can do it in 5 minutes.
What are the steps leading to the right equation? I just want the steps to see if I can work it out alone. Thank you very much.
Notice that C to Midpoint of AB is not necessarily the same as a perpendicular of AB, therefore your entire problem remains.
Let the Midpoint of AB be M(X,Y) and you have already found that answer to be
Finding the Gradient is easy, since we know two points on the line.
Equation of the Line
Hope this helps