Geo formulas and ways to prove trapizoids and kites

Mid point formula

M = ((x1 + x2)/2, (y1 + y2)/2).

Slope formula

m = (y2 - y1) / (x2 - x1).

Distance Formula

d = √((x2 - x1)² + (y2 - y1)²).

Isosceles Trapezoid

A trapezoid with at least one pair of parallel sides and the non-parallel sides being equal in length. It has congruent base angles and symmetry about the line that bisects the bases.

Kite

A quadrilateral with two distinct pairs of adjacent sides that are equal in length.

Dilation Formula (Not Centered)

(x', y') = (k(x - h) + h, k(y - k) + k), where k is the scale factor and (h, k) is the center of dilation.

Line Reflection x axis

(x, y) to (x, -y).

Line Reflection y axis

(x, y) to (-x, y).

Line Reflection y=x

(x, y) to (y, x).

Line Reflection y=-x

(x, y) to (-y, -x).

Rotation 90 degrees ccw

(x, y) to (-y, x).

Rotation -90 degrees ccw

(x, y) to (y, -x).

Rotation 180 degrees ccw

(x, y) to (-x, -y).