Answer:
-2 or 14
Step-by-step explanation:
You are given two points A(7,6) and B(-1,y). These two points are 10 units away from each other.
If points A and B have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2),[/tex] then the distance between these points is
[tex]AB=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case,
[tex]AB=\sqrt{(7-1)^2+(6-y)^2}[/tex]
Since AB = 10 units, we have
[tex]\sqrt{(7-1)^2+(6-y)^2}=10\\ \\\sqrt{6^2+(6-y)^2}=10\\ \\36+(6-y)^2=100\ [\text{Squared the whole equation}]\\ \\(6-y)^2=100-36\\ \\(6-y)^2=64\\ \\6-y=8\ \text{or}\ 6-y=-8\\ \\y=6-8\ \text{or}\ y=6+8\\ \\y=-2\ \text{or}\ y=14[/tex]
So, we get two points [tex]B_1(1,-2)[/tex] and [tex]B_2(1,14)[/tex]
