Let y represent the y-coordinate of point A.
We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)
The distance between point A and Point B is 13 units.
We will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let point A [tex](0,y)=(x_2-y_2)[/tex] and point A [tex](5,1)=(x_1,y_1)[/tex].
Upon substituting coordinates of both points in distance formula, we will get:
[tex]13=\sqrt{(0-5)^2+(y-1)^2}[/tex]
[tex]13=\sqrt{25+y^2-2y+1}[/tex]
[tex]13=\sqrt{y^2-2y+26}[/tex]
Let us square both sides as:
[tex]13^2=(\sqrt{y^2-2y+26})^2[/tex]
[tex]169=y^2-2y+26[/tex]
[tex]169-169=y^2-2y+26-169[/tex]
[tex]0=y^2-2y-143[/tex]
[tex]y^2-2y-143=0[/tex]
Upon splitting the middle term, we will get:
[tex]y^2-13y+11y-143=0[/tex]
[tex]y(y-13)+11(y-13)=0[/tex]
[tex](y-13)(y+11)=0[/tex]
Now we will use zero product property.
[tex](y-13)=0, (y+11)=0[/tex]
[tex]y=13, y=-11[/tex]
Therefore, the possible coordinates of point A would be [tex](0,-11)[/tex] and [tex](0,13)[/tex].
