Question

The co - ordinate of base (BC ) of the isosceles triangle ABC are given by B(1 , 3) and C (-2 , 7 ) . Which of the following points can be the possible co - orientat of the vertex A

• A. $[-7,\frac{1}{8}]$
• B. (1 , 6 )
• C. $[-\frac{1}{2},5]$
• D. $[\frac{5}{6},6]$

Answer 1

Answer: (A), (D)

The correct options are
A $[-7,\frac{1}{8}]$
D $[\frac{5}{6},6]$

If A be (x , y ) then (AB) = AC as $△$ ABC are isoceles
$\therefore A{B}^2=A{C}^2\Rightarrow$ 6x - 8y + 43 = 0
clearly the points given (i)(iii) , (iv) satisfy the above relation . The points $(-\frac{1}{2},5)$ begin the mid - point of BC cannot be the point A . Hence (i)(iv)