If the distance between point (1,1) and point (a,-3) is 5, what is the value of a?

Question

If the distance between point (1,1) and point (a,-3) is 5, what is the value of a?

Answer 1

To find the distance between two points, use the distance formula:

     d = √( (x₂-x₁)² + (y₂-y₁)² )

 

5 = √( (a-1)² + (-3-1)² )

25 = (a-1)² + (-3-1)²    [square both sides]

25 = (a² -2a + 1) + 16              [use F-O-I-L]

a² - 2a - 8 = 0                           [collect terms; switch sides]

(a-4)(a+2) = 0              [either factor or use quadratic formula]

 

Either a-4=0  or else  a+2=0           [Multiplicative Property of Zero]

Either a=4  or else a=-2

 

The distance between points (1,1) and (4,-3) is 5.

The distance between points (1,1) and (-2,-3) is 5. 

Answer 2

Apply the distance formula to find a.

 

5 = √[(a - 1)² + (-3 - 1)²]

 

25 = (a - 1)² + 16

 

9 = (a - 1)²

 

Two solutions:

 

3 = a - 1 ⇒ a = 4

-3 = a - 1 ⇒ a = -2

Answer 3

√{(1-a)²+(1-[-3])²}=5 using the distance formula

square both sides

(1-a)²+(1+3)²=25

1-2a+a²+16=25

1-2a+a²+16-25=0

a²-2a-8=0

factor

(a-4)(a+2)=0

a-4=0

a=4

a+2=0

a=-2

there are 2 answers; a=4 or a=-2