Final answer:
To find the values of p that satisfy the given conditions, we use the distance formula to calculate the distance between the points (5, 2) and (11, p). Simplifying the equation and solving for p, we find that the values of p that satisfy the conditions are 10 and -6.
Step-by-step explanation:
To find the values of p that satisfy the given conditions, we need to calculate the distance between the points (5, 2) and (11, p) using the distance formula. The distance formula is given by:
d = √((x2-x1)^2 + (y2-y1)^2)
Plugging in the values, we have:
d = √((11-5)^2 + (p-2)^2) = 10
Simplifying the equation and solving for p, we get:
(11-5)^2 + (p-2)^2 = 100
36 + (p-2)^2 = 100
(p-2)^2 = 64
p-2 = ±8
p = 10 or -6
Therefore, the values of p that satisfy the given conditions are 10 and -6.