Question

Find a point P on y-axis which is equivalent from point A(4,8) and B(-6,6)
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Answer 1

Solution :-

Let the coordinates of the point P be ( x , y ).

Given that, the point lies on y-axis.

So, x coordinate of the point = 0

The point P is equivalent from A( 4 , 8 ) and B( -6 , 6 ).

That is,

PA = PB

$\boxed{\bf Distance \ formula = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }$

$\longrightarrow \sf PA = PB \\\\\longrightarrow \sqrt{(0-4)^2+(y-8)^2} = \sqrt{(0+6)^2+(y-6)^2} \\\\\longrightarrow (0-4)^2+(y-8)^2=(0+6)^2+(y-6)^2 \\\\\longrightarrow 4^2+y^2+8^2 + 2 \times y \times 8 = 6^2+y^2+6^2-2 \times y \times 6 \\\\\longrightarrow 16+64-16y = 36+36- 12y \\\\\longrightarrow 80-16y = 72-12y \\\\\longrightarrow -16y+12y = 72-80 \\\\\longrightarrow -4y = - 8 \\\\\longrightarrow \bf y = 2$

Coordinates of the point P = ( 0 , 2 )