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 problem gives and solving for #a# gives:
#4 = sqrt((color(red)(a) - color(blue)(1))^2 + (color(red)(1) - color(blue)(1))^2)#
#4 = sqrt((color(red)(a) - color(blue)(1))^2 + 0^2)#
#4 = sqrt((color(red)(a) - color(blue)(1))^2 + 0)#
#4 = sqrt((color(red)(a) - color(blue)(1))^2#
#4 = color(red)(a) - color(blue)(1)# and #4 = -(color(red)(a) - color(blue)(1))# (Note: The square root of a term always produces a negative and positive result)
Solution 1)
#4 = a - 1#
#4 + color(red)(1) = a - 1 + color(red)(1)#
#5 = a - 0#
#5 = a#
#a = 5#
Solution 2)
#4 = -(a - 1)#
#4 = -a + 1#
#4 - color(red)(1) = -a + 1 - color(red)(1)#
#3 = -a + 0#
#3 = -a#
#color(red)(-1) xx 3 = color(red)(-1) xx -a#
#-3 = a#
#a = -3#
Solution: #a# can be either #5# or #-3#
