How do you find the value of a given the points (-5,3), (-3,a) with a distance of #sqrt5#?

Question

1171 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-03T14:50:20

#a=2# or #a=4#

The distance between two points #(x_1, y_1)# and #(x_2, y_2)# is given by:

#color(magenta)(d = sqrt((y_2 - y_1)^2 + (x_2 - x_1)^2)#

Therefore:

#sqrt(5) = sqrt((a - 3)^2 + (-3 - (-5))^2)#

Square both sides:

#(sqrt(5))^2 = (sqrt((a - 3)^2 + 4))^2#

#5 = (a - 3)^2 + 4#

#5 - 4 = (a- 3)^2#

#1 = (a - 3)^2#

Hence either #a-3=1# i.e. #a=4#

or #a-3=-1# i.e. #a=2#

Hopefully this helps!