Question

If (2, 0) and (3, 1) are the vertices of base of a triangle then the locus of its vertex if area of triangle is unity is

• A. x – y = 0
• B. x – y – 4 = 0
• C. (x – y) (x – y – 4) = 0
• D. None of these

Answer 1

Answer: (C)

(x – y) (x – y – 4) = 0

Answer 2

DABC = ± 1

$\frac { 1 } { 2 }$ $\left| \begin{matrix} 2 & 3 & h & 2 \\ 0 & 1 & k & 0 \end{matrix} \right|$ = ± 1

k – h + 2 = ± 2

taking positive

k – h = 0 h – k = 0

hence x – y = 0

taking negative

h – k – 4 = 0 hence x – y – 4 = 0

(x – y) (x – y – 4) = 0