Question

U6 L6
Finding the distance between 2 points in the coordinate plane
Distance Formula:

Pythagorean Theorem:

Answer 1

The distance between two points (x1, y1) and (x2, y2) in the coordinate plane can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

This formula is derived from the Pythagorean Theorem, where the distance between the two points is the hypotenuse of a right triangle with the horizontal and vertical distances between the points as its legs:

d
|\
(y2-y1) | \
| \
| \
| \
(x2-x1) | \
|______\
(x2-x1)

By substituting the horizontal and vertical distances between the points into the formula, we can calculate the distance between the two points.

Answer 2

So what’s the pyagorean formula

Answer 3

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In other words, for a right triangle with sides of lengths a, b, and c (where c is the hypotenuse), the formula is:

a² + b² = c²

This formula can be used to find the length of any side of a right triangle when the lengths of the other two sides are known. It is the basis for the distance formula in the coordinate plane, as explained before.