Question

Geometry distance formula

Answer 1

The distance formula in geometry is used to find the straight-line distance between two points in a coordinate plane.

Step-by-step explanation:

The subject of this question is Mathematics and the specific topic is Geometry. In geometry, the distance formula is used to find the straight-line distance between two points in a coordinate plane. The formula is derived from the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

The distance formula can be expressed as: d = √((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Answer 2

A(-4, 2) and B(3, -2).

I will do number 2.

Let d(A, B) = distance between the two points.

d(A, B) = sqrt{(3 -(-4))^2 + (-2-2)^2}

d(A, B) = sqrt{(3 + 4))^2 + (-2-2)^2}

d(A, B) = sqrt{(7)^2 + (-4)^2}

d(A, B) = sqrt{49 + 16}

d(A, B) = sqrt{65}

Done!