SOLUTION: The point (5,y) is five units away from the point (2,70). What are the two possible values of y?

Question 598070: The point (5,y) is five units away from the point (2,70). What are the two possible values of y?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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Use the distance formula to find the distance between two points. The two different values of y will give you a point above and and a point below (2,70).
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The distance formula is

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Let (x[1],y[1])=(2,70).
Let (x[2],y[2])=(5,y).
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Substitute 5 for D and the known values for each point.

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Simplify and solve for y.

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Square both sides of the equation to clear the square root.

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Set the polynomial equal to zero, and factor.

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We can use the quadratic formula or the factoring method to solve. 4884 looks like a friendly number to I would try to factor it.
If I can't find factors right away, I switch to the quadratic formula. The Q.F. works for every quadratic, but not every quadratic is factorable.
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; We want two factors with a sum of 140, and a product of 4884. I played around with the prime factors and got -2*3*11=-66 and -2*37=-74. So,
OR
OR
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Therefore, the two points are (5,66) and (5,74).
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Check your work for accuracy.
Distance between (2,70) and (5,66).

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Distance between(2,70) and (5,74).

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That's it! Feel free to email via gmail if you have questions about the solution
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Ms.Figgy
math.in.the.vortex@gmail.com
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