Given the vertices of the triangle: A (3; 5), B (-3; 3), C (5; -8). Determine the length of the median drawn from the vertex C.

| February 20, 2021 | education

The coordinates of point C are known. It is necessary to determine the coordinates (xd; yd) of point D. According to the definition: “The median of a triangle is a segment connecting the apex of a triangle with the middle of the opposite side of this triangle.” Hence, point D is the midpoint of segment AB.
Here is the formula for calculating the coordinates (xs; ys) of the midpoint of the segment with the ends A (xa; ya) and B (xb; yb) on the plane: xs = (xа + xb) / 2; ys = (yа + yb) / 2. According to this formula, we calculate the coordinates (xd; yd) of point D: xd = (3 + (–3)) / 2 = 0; yd = (5 + 3) / 2 = 4.
Now let’s define the length of the median CD as the distance between the points C (5; –8) and D (0; 4) according to the formula for calculating the distance between two points A (xa, ya) and B (xb, yb) on the plane: AB = √ [ (xb – xa) ^ 2 + (yb – ya) ^ 2]. We have: CD = √ [(0 – 5) ^ 2 + (4 – (–8)) ^ 2] = √ (25 + 144) = 13.
Answers: 13.



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