Analysing Triangle Vertices and Bisectors

... Part 1 The diagram shows a triangle with vertices O(0,0), A(2,6) and B(12,6). The perpendicular bisectors of OA and AB meet a C. (a) In order to write down the perpendicular bisector of the line joining the points A(2,6) and B(12,6), I need to find the line's mid-point. The mid-point of the line joining P(x1, y1) to Q(x2, y2) has the co-ordinates ( ) So the co-ordinates of the midpoint of AB are ( ) = (7,6) As the two points A(2,6) and B(12,6) have the same y-value, the gradient of the line joining the points is 0. This means that the line's perpendicular bisector also has a gradient of 0. Thus the equation of the bisector is x = 7 (b) To find the equation of the perpendicular bisector of the line joining the points O (0,0) and A(2,6), I again need to find the co-ordinates of the mid-point of OA. The gradient, and hence that

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