Distance Between Points

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

Using the distance formula: $$d = \text{sqrt}((3 - 0)^2 + (4 - 0)^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

Using the distance formula: $$d = \text{sqrt}((4 - (-3))^2 + (-4 - 4)^2) = \text{sqrt}(7^2 + (-8)^2) = \text{sqrt}(49 + 64) = \text{sqrt}(113)$$ .

To round to the nearest hundredth, look at the third decimal place. If it's 5 or more, round up the second decimal place by one. If it's less than 5, keep the second decimal place the same.

Using the distance formula: $$d = \text{sqrt}((-3.7 - (-8.2))^2 + (-4.8 - (-6.4))^2) = \text{sqrt}(4.5^2 + 1.6^2) = \text{sqrt}(20.25 + 2.56) = \text{sqrt}(22.81) \text{ which is approximately } 4.78$$ .

Using the distance formula: $$d = \text{sqrt}((24 - 11)^2 + (21 - 15)^2) = \text{sqrt}(13^2 + 6^2) = \text{sqrt}(169 + 36) = \text{sqrt}(205)$$ .

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is the basis for the distance formula.

The perimeter of a parallelogram is calculated as: $$P = 2(a + b)$$ , where 'a' and 'b' are the lengths of the two different sides.

Using the latitude and longitude difference: Distance = $$|37.6 - 39.9| \times 68 + |126.0 - 116.4| \times 68 = 2.3 \times 68 + 9.6 \times 68 = 671.3 \text{ miles}$$ .

The formula is: $$d = \text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$ .