The point A is shown on the unit grid below.

The coordinates of

From the diagram, the coordinates of are

the distance from to is

Since also lies on the grid, and should be integers and should satisfy the distance relationship

There is a way to get from Pythagoras rule

Which means we can either say

Therefore B is either at location or

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Coordinates of point B are (3, 5) and (5, 3).

Step-by-step explanation:

Coordinates of point A → (1, 1)

Let the coordinates of point B are (x', y')

Formula for the distance between points (x, y) and (x', y') is,

d =

AB =

20 = (x - 1)² + (y - 1)²

Since point A lies on the intersection of two grid lines in the 1st quadrant, x and y must be the positive whole number.

For x = 0,

20 = (0 - 1)² + (y - 1)²

(y - 1)² = 20 - 1

y = 1 + √19

But y can't be a decimal, therefore, x = 0 is not the answer.

For x = 1

20 = (1 - 1)² + (y - 1)²

20 - 1 = (y - 1)²

y = 1 + √19

Not a whole number, so can't be the solution.

For x = 2,

20 = (2 - 1)² + (y - 1)²

y = 1 + √19

Not a whole number, therefore, not the answer.

For x = 3,

20 = (3 - 1)² + (y - 1)²

20 - 4 = (y - 1)²

y = 1 + √16

y = 5

Therefore, (3, 5) are coordinates of the point B.

For x = 4,

20 = (4 - 1)² + (y - 1)²

20 = 9 + (y - 1)²

y = 1 + √11

For x = 5,

20 = (5 - 1)² + (y - 1)²

20 - 16 = (y - 1)²

4 = (y - 1)²

y = 3

Therefore, (5, 3) the coordinates of point B.