Distance between Two Points

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

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

The hypotenuse is the longest side of a right triangle, opposite the right angle.

The legs of a right triangle are the two sides that form the right angle.

The Pythagorean theorem states that in a right triangle, $$a^2 + b^2 = c^2$$ , where c is the length of the hypotenuse.

Using the Pythagorean theorem: $$c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$$ .

Using the distance formula: $$d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ .

To round to the tenths place, look at the hundredths place. If it's 5 or more, round up; if it's less than 5, keep the tenths place the same.

The distance is 4 units, calculated as $$d = \sqrt{(2 - 2)^2 + (7 - 3)^2} = \sqrt{0 + 16} = 4$$ .

Two points are equidistant from a third point if they are the same distance away from that point.