Algebra word problem

Question

Find all points having an x coordinate of 3 whose distance from the point (2,7) is 13

Answer 1

There may be a typo in your problem statement. Likely, for Algebra 1, it is either:

x-coordinate of (-3)

or

distance from the point (-2,7)

but not both.

With this editing change, a 5-12-13 (a common Pythagorean Triple) triangle is formed. The y-value is either 7+12 or 7-12. That gives the two points

(-3,19) and (-3,-5) <============[ for x-coordinate of (-3) and point (2,7)]

or else

(-2,19) and (-2,-5) <===========[ for x-coordinate of 3 and point (-2,7) ]

but not both.

Answer 2

There are two ways you can tackle this problem and they both have the same formula. You could recognize that graphing an object with the same distance in all directions from a point is a circle so we could use the circle equation which will give us (x-2)²+(y-7)²=13². From here, we plug in x=3 and solve for y.

The alternative method is to use distance formula. √((x-2)²+(y-7)²)=13. Then plug in x=3.

But I think you can see the distance formula is actually the formula for a circle (it is also the Pythagorean Theorem). Either way, we can then solve for y.

(3-2)²+(y-7)²=13² simplifies to (y-7)²=168. This simplifies to y=7±√168 or y=7±2√42