Question
The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y –3 = 0 and the third side passes through the point (1, -10). The equation of the third side is
Answer: Option C
:
C
Any line through (1, - 10) is given by y + 10 = m(x - 1)
Since it makes equal angle ′α′ with the given lines 7x – y + 3 = 0 and x + y – 3 = 0, therefore
tanα=m−71+7m=m+11+m(−1)⇒m=13 or −3
Hence the two possible equations of third side are 3x + y + 7 = 0 and x - 3y - 31 = 0.
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:
C
Any line through (1, - 10) is given by y + 10 = m(x - 1)
Since it makes equal angle ′α′ with the given lines 7x – y + 3 = 0 and x + y – 3 = 0, therefore
tanα=m−71+7m=m+11+m(−1)⇒m=13 or −3
Hence the two possible equations of third side are 3x + y + 7 = 0 and x - 3y - 31 = 0.
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