Answer:
(5,2) and (5,10)
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]points\ (2,6),(5,y)\\d=5[/tex]
substitute in the formula
[tex]5=\sqrt{(y-6)^{2}+(5-2)^{2}}[/tex]
solve for y
[tex]5=\sqrt{(y-6)^{2}+(3)^{2}}[/tex]
[tex]5=\sqrt{(y-6)^{2}+9}[/tex]
square both sides
[tex]25=(y-6)^{2}+9[/tex]
[tex](y-6)^{2}=25-9[/tex]
[tex](y-6)^{2}=16[/tex]
square root both sides
[tex]y-6=\pm4[/tex]
[tex]y=6\pm4[/tex]
[tex]y=6+4=10[/tex]
[tex]y=6-4=2[/tex]
therefore
The points are
(5,2) and (5,10)
