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Question
In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (–2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vertex B and parallel to AC.
Solution
Given, the co-ordinates of vertices A, B and C of a triangle ABC are (4, 7), (–2, 3) and (0, 1) respectively.
Let AD be the median through vertex A.
Co-ordinates of the point D are
`((-2 + 0)/2, (3 + 1)/2)`
(–1, 2)
∴ Slope of AD = `(2 - 7)/(-1 - 4) = (-5)/(-5) = 1`
The equation of the median AD is given by:
y − y1 = m(x − x1)
y − 2 = 1(x + 1)
y − 2 = x + 1
y = x + 3
The slope of the line which is parallel to line AC will be equal to the slope of AC.
Slope of AC = `(1 - 7)/(0 - 4) = (-6)/(-4) = 3/2`
The equation of the line which is parallel to AC and passes through B is given by:
`y - 3 = 3/2(x + 2)`
2y − 6 = 3x + 6
2y = 3x + 12
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