Question

Area of triangle is 5. Its two vertices are (2, 1) and (3, –2). Third vertex is on line y = x + 3. That vertex will be :

• A. $\left( \frac{7}{2},\frac{13}{2} \right)$
• B. (8, 14)
• C. $\left( \frac{8}{3},\frac{5}{3} \right)$
• D. $\left( \frac{7}{3},\frac{9}{7} \right)$

Answer 1

Answer: (A)

$\left( \frac{7}{2},\frac{13}{2} \right)$

Answer 2

Let third vertex is (h, h + 3)

Now, $\frac{1}{2}\left| \begin{matrix} h & h + 3 & 1 \\ 2 & 1 & 1 \\ 3 & - 2 & 1 \end{matrix} \right| = \pm 5$

Ž 3h + (h + 3) – 7 = ± 10 Ž 4h – 4 = ± 10

Ž h = 7/2, – 3/2 Ž (7/2, 13/2), (–3/2, 3/2)