A triangle has vertices A(-3,5), B(7,9) and C(2,11). What is the equation of the median that passes through the vertex C?
First we can to start by making a sketch of the triangle since it may be easier to visualise the problem. Since the median of a triangle is a line that joins a vertex to the midpoint of the opposite side, we can draw this onto our sketch. The first step required to tackle this problem is to calculate the midpoint of the line AB that the median is bisecting. This is done by applying the midpoint formula,M = ((x1+ x2)/2 , (y1 + y2)/2)where x1 and y1 are the coordinates of A, and x2 and y2 are the coordinates of B.Inputting these values into the equation results in a midpoint of (2,7).Since we know two points on the line CM, we can find its gradient usingm = (y2 - y1)/(x2 - x1)and thus giving us a denominator of 0, showing that the median is a vertical line. All vertical lines have a constant gradient and therefore this is the x-coordinates of both points, x = 2This gives us the equation for the median bisecting AB and passing though C, x = 2, as required.
