Answer:
x = -4 , 4
Step-by-step explanation:
The point (x,4) is equidistant from (0,1) and line y=-1
y=-1, it is horizontal line.
Let point on line be (x,-1)
Distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between (x,4) and (x,-1) = Distance between (x,4) and (0,1)
[tex]\sqrt{(x-x)^2+(4+1)^2}=\sqrt{(x-0)^2+(4-1)^2[/tex]
[tex]\sqrt{5^2}=\sqrt{x^2+3^2[/tex]
[tex]25=x^2+9[/tex]
[tex]x^2=16[/tex]
[tex]x=\pm \sqrt{16}[/tex]
[tex]x=\pm 4[/tex]
hence, the value of x is 4 and -4
