Final answer:
To find the value of 'a' in the coordinates N(12,a), we need to calculate the length of MN.
Step-by-step explanation:
To find the value of 'a' in the coordinates N(12,a), we need to calculate the length of MN.
Using the distance formula, we can find the distance between the points M(2,-3) and N(12,a):
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that d = 5 * sqrt(5), we substitute the values:
5 * sqrt(5) = sqrt((12 - 2)^2 + (a - (-3))^2)
Simplifying the equation:
25 * 5 = (10)^2 + (a + 3)^2
125 = 100 + (a + 3)^2
(a + 3)^2 = 125 - 100
(a + 3)^2 = 25
Taking the square root of both sides:
a + 3 = 5 or a + 3 = -5
a = 5 - 3 or a = -5 - 3
a = 2 or a = -8