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Question
P(3, 4), Q(7, –2) and R(–2, –1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.
Solution
Let median through R be RX.
We know that, the median, RX through R will bisect the line PQ.
By Mid-point formula,
Mid-point = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
The co-ordinates of point X are
`((3 + 7)/2, (4 +(-2))/2)`
= `(10/2, 2/2)`
= (5, 1)
By formula,
Slope = `(y_2 - y_1)/(x_2 - x_1)`
Substituting values we get,
Slope of RX = `(1 - (-1))/(5 - (-2)) = 2/7`
Then, the required equation of the median RX is given by
`=>` y − y1 = m(x − x1)
`=> y - (-1) = 2/7[x - (-2)]`
`=> y + 1 = 2/7(x + 2)`
`=>` 7(y + 1) = 2(x + 2)
`=>` 7y + 7 = 2x + 4
`=>` 7y = 2x – 3
Hence, equation of the median through R is 7y = 2x – 3.
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