Question

2. The point on Y-axis equidistant from (–3, 4) and (7, 6) is _________: (a) (0, 15) (b) (0, 14) (c) (0, 13) (d) None of these​

Answer 1

class? tell me in comment

Answer 2

Given,

Point on Y-axis equidistant from (–3, 4) and (7, 6).

Solution,

Consider the point is $\[\left( {x,y} \right)\]$.

$\[\sqrt {{{\left( {x + 3} \right)}^2} + {{\left( {y - 4} \right)}^2}} = \sqrt {{{\left( {x - 7} \right)}^2} + {{\left( {y - 6} \right)}^2}} \]$

Squaring on both side,

$\[\begin{array}{l}{\left( {x + 3} \right)^2} + {\left( {y - 4} \right)^2} = {\left( {x - 7} \right)^2} + {\left( {y - 6} \right)^2}\\ \Rightarrow {x^2} + 6x + 9 + {y^2} - 8y + 16 = {x^2} - 14x + 49 + {y^2} - 12y + 36\\ \Rightarrow 20x + 4y + 25 - 49 - 36 = 0\\ \Rightarrow 5x + y = 15\end{array}\]$

On Y-axis value of x coordinate will be zero,

$\[\begin{array}{l}5x + y = 15\\ \Rightarrow 5 \times 0 + y = 15\\ \Rightarrow y = 15\end{array}\]$

Hence the coordinate will be $\[\left( {0,15} \right)\]$.

The correct option is (a), i.e. $\[\left( {0,15} \right)\]$.