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Question
From the given figure, find:
- the co-ordinates of A, B and C.
- the equation of the line through A and parallel to BC.
Solution
i. A = (2, 3), B = (−1, 2), C = (3, 0)
ii. Slope of BC = `(0-2) /(3+1) = -2/4 = -1/2`
Slope of required line which is parallel to BC = Slope of BC = `-1/2`
(x1, y1) = (2, 3)
The required equation of the line through A and parallel to BC is given by:
y – y1 = m(x – x1)
`=> y - 3 = -1/2(x - 2)`
`=>` 2y − 6 = −x + 2
`=>` x + 2y − 6 − 2 = 0
`=>` x + 2y − 8 = 0
`=>` x + 2y = 8
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