The equation of two equal sides of an isosceles triangle are 7x−y+3=0 and x+y−3=0. If the third side passes through (1,−10) and its slope is negative, then the equation of the third side is
A
3x+y+7=0
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B
2x+y+8=0
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C
3x+y−7=0
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D
x−3y−31=0
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Solution
The correct option is A3x+y+7=0 Let m be the slope of the third line. Equation of the line with slope m and passing through (1,−10) is y+10=m(x−1) Since the third line makes equal angle with the given two lines, ∣∣∣m−71+7m∣∣∣=∣∣∣m−(−1)1−m∣∣∣ Taking positive signs, we get m2+1=0 (Not possible)
Hence, m−71+7m=−(m+11−m) ⇒3m2+8m−3=0 ⇒(3m−1)(m+3)=0 ⇒m=13 or m=−3 But m<0 ∴ Equation of the third line is 3x+y+7=0