Mathematics
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.
Straight Line Eq
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Answer
(i) Let the slope of BC be m1. Slope of BC is given by,
Hence, the slope of BC is .
(ii) Let slope of line perpendicular to BC be m2
So,m1 × m2 = -1
⇒ × m2 = -1
⇒ m2 =
Equation of the line having the slope = and passing through A(3, 8) can be given bu point slope formula i.e.,
⇒ y - y1 = m(x - x1)
⇒ y - 8 = (x - 3)
⇒ 8(y − 8) = 7(x − 3)
⇒ 8y − 64 = 7x − 21
⇒ 7x − 8y − 21 + 64 = 0
⇒ 7x − 8y + 43 = 0.
Hence, the equation of the required line is 7x - 8y + 43 = 0.
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