The formula for calculating the distance between two points is:
d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)
Substituting the values from the points in the problem gives:
10 = sqrt((color(red)(-5) - color(blue)(a))^2 + (color(red)(2) - color(blue)(-6))^2)
10 = sqrt((color(red)(-5) - color(blue)(a))^2 + (color(red)(2) + color(blue)(6))^2)
10^2 = (sqrt((color(red)(-5) - color(blue)(a))^2 + (color(red)(2) + color(blue)(6))^2))^2
100 = (color(red)(-5) - color(blue)(a))^2 + (color(red)(2) + color(blue)(6))^2
100 = (color(red)(-5) - color(blue)(a))^2 + 8^2
100 = (color(red)(-5) - color(blue)(a))^2 + 64
100 - color(red)(64) = (color(red)(-5) - color(blue)(a))^2 + 64 - color(red)(64)
36 = (color(red)(-5) - color(blue)(a))^2 + 0
36 = (color(red)(-5) - color(blue)(a))^2
sqrt(36) = sqrt((color(red)(-5) - color(blue)(a))^2)
6 = +-(-5 - a)
Solution 1)
6 = -(-5 - a)
6 = 5 + a
-color(red)(5) + 6 = -color(red)(5) + 5 + a
1 = 0 + a
1 = a
a = 1
Solution 2)
6 = -5 - a
color(red)(5) + 6 = color(red)(5) - 5 - a
11 = 0 - a
11 = -a
color(red)(-1) xx 11 = color(red)(-1) xx -a
-11 = a
a = -11
The solutions are a = -11 or a = 1
