Question

Let B and C be points (12, 19) and (23, 20) respectively. Let A $(\alpha ,\beta )$ be a point such that area of triangle formed by the points A, B and C is 70. Also the slope of the median through A is – 5.

Match the following:
$\begin{array}{cccc}& ColumnI& & ColumnII\\ \left(a\right)& Apossiblevalue\alpha +\beta is& \left(p\right)& 2\\ \left(b\right)& Apossiblevalue\beta -2\alpha is& \left(q\right)& 27\\ \left(c\right)& Apossiblevalue3\alpha -\beta -11is& \left(r\right)& -33\\ \left(d\right)& Apossiblevalue\alpha -2\beta +16is& \left(s\right)& 47\\ & & \left(t\right)& 28\end{array}$

• A. A) $\to$ p, r B) $\to$ q,s C) $\to$ s D) $\to$ q
• B. A) $\to$ s,q B) $\to$ p,r C) $\to$ p D) $\to$ r
• C. A) $\to$ r B) $\to$ q, s C) $\to$ q D) $\to$ p
• D. A) $\to$ p B) $\to$ p, q C) $\to$ q, s D) $\to$ r

Answer 1

The correct option is B A) $\to$ s,q B) $\to$ p,r C) $\to$ p D) $\to$ r

$|-197+11\beta -\alpha |=140,2\beta +10\alpha =214$
Considering the equations $11\beta –\alpha =337,2\beta +10\alpha =214$
We get $\alpha =15,\beta =22$ gives the conclusions