12.6 Distance Between Points

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

The distance formula calculates the straight-line distance between two points in a 2D coordinate system.

To round to the nearest tenth, look at the hundredths place. If it's 5 or more, round up; if it's less than 5, round down.

The distance is 5, calculated using the distance formula: $$d = \text{sqrt}((3 - 0)^2 + (4 - 0)^2) = 5$$ .

The distance is approximately 2.83, calculated as $$d = \text{sqrt}((1 - (-1))^2 + (1 - (-1))^2) = \text{sqrt}(8) = 2\text{sqrt}(2)$$ .

The square root ensures that the distance is a non-negative value, as distance cannot be negative.

Use the distance formula and simplify the expression without calculating the square root.

The distance is 5, calculated as $$d = \text{sqrt}((5 - 5)^2 + (10 - 5)^2) = 5$$ .

The exact distance is $$\text{sqrt}(96)$$ .

The exact distance is $$\text{sqrt}(205)$$ .