Just for my notes how do we use coordinates to classify polygons on the coordinate plane?

Explanation:

Polygons are classified by ...

The number of coordinate pairs will define the number of vertices.

The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).

If the differences between adjacent coordinate pairs are ...

  (∆x, ∆y) = (x2 -x1, y2 -y1)

then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)

It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...

  α = arctan(slope)

The length of a line segment (d) can be found from the Pythagorean theorem:

  d = √((∆x)² +(∆y)²)

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w