Pythagorean Theorem - Distance Between Two Points

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$c^2 = a^2 + b^2$$ .

The distance d between two points can be calculated using the formula: $$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$$ .

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

The hypotenuse is 5.

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

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

A right triangle is a triangle that has one angle measuring 90 degrees.

Yes, because $$10^2 = 6^2 + 8^2$$ (100 = 36 + 64).

Using the distance formula: $$d = \sqrt{((-1) - (-5))^2 + ((-16) - (-8))^2} = \sqrt{16 + 64} = \sqrt{80} = 8.9$$ .

The Pythagorean Theorem is used in various fields such as architecture, construction, and navigation to calculate distances and ensure structures are built correctly.