Question

The area of a triangle is 5. Two of its vertices are (2, 1) and (3, -2). The third vertex is (x, y) where y = x + 3. Then the co-ordinate of the third vertex is

• A. $(\frac{7}{2},\frac{13}{2})or(-\frac{3}{2},\frac{3}{2})$
• B. $(\frac{-7}{2},\frac{13}{2})or(\frac{3}{2},\frac{3}{2})$
• C. $(\frac{1}{2},\frac{3}{2})$
• D. $(\frac{3.}{2},\frac{1}{2})$

Answer 1

The correct option is A $(\frac{7}{2},\frac{13}{2})or(-\frac{3}{2},\frac{3}{2})$

Solve by trial and elimination method.
Putting coordinates in the equation, we find that only option (a) i.e, $(\frac{7}{2},\frac{13}{2})or(-\frac{3}{2},\frac{3}{2})$ satisfies the equation of the line y = x + 3.