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Question
The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find:
(i) Slope of BC
(ii) Equation of a line perpendicular to BC and passing through A.
Solution
A (3, 8) , B(–1, 2) , C(6, –6)
(i) Slope of BC = `(y_2 - y_1) /(x_2- x_1) = (-6 - 2)/(6-(-1)) = (-8)/7`
∴ Slope of BC = - `8/7`
(ii) Slope of line perpendicular to BC `= (-1)/((-8/7)) = 7/8`
Required line ⇒ y - y1 = m(x - x1 )
y - 8 = `7/8 (x-3)`
`8y - 64 = 7x -21`
`7x - 8y + 43 = 0`
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