If the distance between the points (4, p) and (1, 0) is 5, then the value of p…

Solution:

Use the distance formula between (4, p) and (1, 0):

sqrt((4 - 1)^2 + (p - 0)^2) = 5

Square both sides to remove the square root:

1. (4 - 1)^2 + p^2 = 25

2. 9 + p^2 = 25

3. p^2 = 16

4. p = ±4

Therefore the values of p are 4 and -4.

Quick check:

• For p = 4: distance = sqrt(9 + 16) = 5.

• For p = -4: distance = sqrt(9 + 16) = 5.