Find the possible values of a if the points with the given coordinates are the indicated distance apart.
1. (1, a), (3, -2); d=5

Possible values of a =  2.58 and  -6.58.

Step-by-step explanation:

Using the distance formula

√(3- 1)^2 + (-2-a)^2) = 5

(3- 1)^2 + (-2-a)^2 = 25

4 + 4a + a^2 + 4 = 25

a^2  + 4a - 17 = 0

a = [-4 +/- √(4^2 - 4*1*-17) ] / 2

a =  -2 +/- √84 / 2

a =  2.58, -6.58.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2