Answer:
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 = [tex]\sqrt{(x-x')^+(y-y')^2}[/tex]
AB = [tex]\sqrt{(x-1)^+(y-1)^2}[/tex]
[tex]2\sqrt{5}=\sqrt{(x-1)^2+(y-1)^2}[/tex]
[tex](2\sqrt{5})^2=(x-1)^2+(y-1)^2[/tex]
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.
