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Question
Find the equation of the line which satisfy the given condition:
The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
Solution
It is given that the vertices of ΔPQR are P (2, 1), Q (–2, 3), and R (4, 5).
Let RL be the median through vertex R.
Accordingly, L is the mid-point of PQ.
By mid-point formula, the coordinates of point L are given by `((2 - 2)/2, (1 + 3)/2) = (0, 2)`
It is known that the equation of the line passing through points (x1, y1) and (x2, y2) is y - y1 = `(y_2 - y_1)/(x_2 - x_1) (x - x_1)`
Therefore, the equation of RL can be determined by substituting (x1, y1) = (4, 5) and (x2, y2) = 0
Hence, `y - 5 = (2 - 5)/(0 - 4) (x - 4)`
= `y - 5 = (-3)/(-4) (x - 4)`
= 4(y - 5) = 3(x - 4)
= 4y - 20 = 3x - 12
= 3x - 4y + 8 = 0
Thus, the required equation of the median through vertex R is 3x - 4y + 8 = 0
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