Question

A line 4x + y = 1 through A(2, –7) meets a line BC,

3x – 4y + 1 = 0 at B and AB = AC. Slope of the line AC is

• A. – $\frac { 47 } { 81 }$
• B. –$\frac { 53 } { 91 }$
• C. – $\frac { 52 } { 89 }$
• D. None of these

Answer 1

Answer: (C)

– $\frac { 52 } { 89 }$

Answer 2

Suppose slope of AC is m,

Now, AB = AC; Ž Š B = Š C Ž tan B = tan C

Ž $\left| \frac { m + \frac { 4 } { 3 } } { 1 - \frac { 4 m } { 3 } } \right|$ = $\left| \frac { ( - 4 ) + \frac { 4 } { 3 } } { 1 + ( - 4 ) \left( \frac { - 4 } { 3 } \right) } \right|$

Ž m = – 4 (rejected because of slope of AB) OR $\frac { - 52 } { 89 }$