Distance Between Points on the Coordinate Plane

The distance d is given by the formula: d = $$\text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

Using the distance formula: d = $$\text{sqrt}((7 - 3)^2 + (1 - 4)^2) = \text{sqrt}(16 + 9) = \text{sqrt}(25) = 5$$ .

The distance is 5, calculated as d = $$\text{sqrt}((0 - 0)^2 + (5 - 0)^2) = \text{sqrt}(25) = 5$$ .

Using the distance formula: d = $$\text{sqrt}((5 - 2)^2 + (7 - 3)^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

Using the distance formula: 5 = $$\text{sqrt}((x - 1)^2 + (5 - 2)^2)$$ . Solving gives x = 1 + 4 or x = 1 - 4, so x = 5 or x = -3.

The distance is d = $$\text{sqrt}((0 - (-3))^2 + (0 - (-4))^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

Using the distance formula: d = $$\text{sqrt}((4 - 1)^2 + (5 - 1)^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

The distance is 6, calculated as d = $$\text{sqrt}((2 - 2)^2 + (8 - 2)^2) = \text{sqrt}(0 + 36) = \text{sqrt}(36) = 6$$ .

It represents the horizontal distance between the two points on the x-axis.

It represents the vertical distance between the two points on the y-axis.