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 information from the problem and solving for a gives:
sqrt(50) = sqrt((color(red)(a) - color(blue)(-4))^2 + (color(red)(8) - color(blue)(1))^2)
sqrt(50) = sqrt((color(red)(a) + color(blue)(4))^2 + (color(red)(8) - color(blue)(1))^2)
sqrt(50) = sqrt((color(red)(a) + color(blue)(4))^2 + 7^2)
sqrt(50) = sqrt(a^2 + 8a + 16 + 49)
sqrt(50) = sqrt(a^2 + 8a + 65)
(sqrt(50))^2 = (sqrt(a^2 + 8a + 65))^2
50 = a^2 + 8a + 65
50 - color(red)(50) = a^2 + 8a + 65 - color(red)(50)
0 = a^2 + 8a + 15
0 = (a + 3)(a + 5)
Solution 1:
a + 3 = 0
a + 3 - color(red)(3) = 0 - color(red)(3)
a + 0 = -3
a = -3
Solution 2:
a + 5 = 0
a + 5 - color(red)(5) = 0 - color(red)(5)
a + 0 = -5
a = -5
The Solution Is:
color(red)(a) can be either -3 or -5 for the two points to have a distance of sqrt(50)
