**Q:** Find the possible values of a, if the distance between the points is 5, and the coordinates are (1,1) and

(4,a). Thank you.

**A:** Are you familiar with the distance formula? The distance d, between two points (x1,y1) and (x2,y2) is given by:

In your question, . Rearrange the distance formula to solve for a:

Square both sides to get rid of the square root.

25 = (4-1)^2 + (a-1)^2

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

Do FOIL:

25 = 9 + a^2 -2a + 1

0 = a^2 -2a + 1 + 9 – 25

0 =a^2 -2a -15

Solve by factoring. Think, what are two numbers that multiply to -15 and add up to -2a? The answer? -5 and 3.

0 = (a-5)(a+3)

So either a-5=0, which means a=5, or a+3=0, which means a= -3.

The possible values of a are 5 and -3.

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