 # Equidistant Points 2

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create two points that are equidistant from (4,-1). ### Hint

Which methods are available to determine answers to this problem? What shape is defined by all of the points that are equidistant from (4, -1)?

There are many correct answers to this problem including: (2, 4) and (9, 1) as well as (2, 3), and (8, 1)

Source: Bryan Anderson

## Equations of Circles 1

Directions: Using the integers -9 to 9, at most one time each, fill in the …

1. We worked this problem out and only found 4 possible answers. Do you think there are more than that?

Our other answers were (1,4), (9,2) and (1,3), (8,2).

Thanks!

• there are many more, if you think in terms of slope, any that create perpendicular lines will work; all the points to the left or right two and up one will be the same as going left or right one, then up two. etc

• If remove the limits of only being able to use the digits 1 through 9 at most once, then there are infinite possibilities, but with that limit it place I think Andrew is right. I can only find the two pairs listed above. Any other pairs of points will require repeating a digit or using 0, negatives, or fractions.