Find a if the distance between (6.2) and (0,a) is 10 units Solution Given the distance between the points (0, 6) and ( 2,a) is 10 units. We will use the distance between two points formula to solve. We know that: D (AB) = sqrt[ ( xA-xB)^2 + ( yA-yB)^2 ]. Then, we will substitute. ==> D = sqrt( 6-0)^2 + ( a-2)^2 = 10 ==> sqrt(6^2) +(a-2)^2 = 10 ==> sqrt(36+(a-2)^2] = 10 Now we will square both sides. ==> 36 + (a-2)^2 = 100. Now we will subtract 36 from both sides. ==> (a-2)^2 = 64. Now we will take the root of both sides. ==> (a-2) = +- 8 ==> (a-2) = 8 ==> a= 10 ==> (a-2) = -8 ==> a= -6 Then we have two possible values for a. ==> a1= 10 ==> a2= -6 Then, the points ( 0, -6) and ( 0, 10) are located 10 units from the point (6,2)..

1. Find a if the distance between (6.2) and (0,a) is 10 units
Solution
Given the distance between the points (0, 6) and ( 2,a) is 10 units.
We will use the distance between two points formula to solve.
We know that:
D (AB) = sqrt[ ( xA-xB)^2 + ( yA-yB)^2 ].
Then, we will substitute.
==> D = sqrt( 6-0)^2 + ( a-2)^2 = 10
==> sqrt(6^2) +(a-2)^2 = 10
==> sqrt(36+(a-2)^2] = 10
Now we will square both sides.
==> 36 + (a-2)^2 = 100.
Now we will subtract 36 from both sides.
==> (a-2)^2 = 64.
Now we will take the root of both sides.
==> (a-2) = +- 8
==> (a-2) = 8 ==> a= 10
==> (a-2) = -8 ==> a= -6
Then we have two possible values for a.
==> a1= 10
==> a2= -6
Then, the points ( 0, -6) and ( 0, 10) are located 10 units from the point (6,2).