Question

Find the values of x for which the point (x, −3) is equidistant from (1,−2), and the line y =2.

Answer 1

The value of x will be -11.5

Explanation:

We have given point (x , -3 ) which is equidistant from (1, -2 ) and y =2

And we have to find the value f x

y =2 means the point (0, 2 )

So distance between the point (x ,-3 ) and ( 1 , -2 )

`d=√((x-1)^2+(-3-(-2))^2)=√((x-1)^2+1)`

And distance between point (x ,-3 ) and ( 0 , 2 )

`d=√((x-0)^2+(-3-(2))^2)=√(x^2+25)`

As these distance are equal

So
`√(x^2+25)=√((x-1)^2+1)`

Squaring both side

`{x^2+25}=(x-1)^2+1`

x = -11.5