Rectangle?
The first characteristic of proving a shape a rectangle is that the diagonals are congruent. To prove this using coordinate geometry, you find the length of the diagonal using the distance formula.

The second characteristic of proving a shape a rectangle is that all angles are 90 degrees. To prove this using coordinate geometry, you find the slope of the consecutive sides using the slope formula. If the slopes are the negative inverse of eachother than they are perpendicular therefore forming 90 degree angles.

Example: Is FGHJ a rectangle?
F (-4,-1) G(-2,-5) H(4,-2) J(2,2)
You can either prove it is a rectangle by proving it has 4 90 degree angles by slope formula or by proving its diagonals are congruent by distance formula.
For slope, find the slope of GH and FG to see if they are perpendicular. Then find the slope of HJ and FJ to see if they are perpendicular.
For distance, find the length of diagonals FH and JG to see if they are congruent.
The answer is yes.

Rhombus?
The first characteristic of proving a shape a rhombus is if it has 4 congruent sides. To prove this using coordinate geometry you find the length of the sides using the distance formula.

The second characteristic of proving a shape a rhombus is if its diagonals are perpendicular. To prove this using coordinate geometry you find the slope of the diagonal to see if they are perpendicular or the negative inverse.

Example: Is ABCD a rhombus?
A(-2,-1) B(-1,3) C(3,2) D(2,-2)
You can either prove its a rhombus by using slope formula to prove that the diagonals are perpendicular or by using distance formula to prove that it has 4 congruent sides.
For slope, find the slope of diagonals AC and BD to see if they are perpendicular to each other.
For distance, find the distance of each side, AB, BC, CD, and DA to see if they are congruent.
The answer is yes.

Square?
To prove that a shape is a square using coordinate geometry you need to prove one characteristic of a rectangle and one characteristic of a rhombus.

Katherine Haddock// Feb 22, 2006 at 9:22 pmRectangle?

The first characteristic of proving a shape a rectangle is that the diagonals are congruent. To prove this using coordinate geometry, you find the length of the diagonal using the distance formula.

The second characteristic of proving a shape a rectangle is that all angles are 90 degrees. To prove this using coordinate geometry, you find the slope of the consecutive sides using the slope formula. If the slopes are the negative inverse of eachother than they are perpendicular therefore forming 90 degree angles.

Example: Is FGHJ a rectangle?

F (-4,-1) G(-2,-5) H(4,-2) J(2,2)

You can either prove it is a rectangle by proving it has 4 90 degree angles by slope formula or by proving its diagonals are congruent by distance formula.

For slope, find the slope of GH and FG to see if they are perpendicular. Then find the slope of HJ and FJ to see if they are perpendicular.

For distance, find the length of diagonals FH and JG to see if they are congruent.

The answer is yes.

Rhombus?

The first characteristic of proving a shape a rhombus is if it has 4 congruent sides. To prove this using coordinate geometry you find the length of the sides using the distance formula.

The second characteristic of proving a shape a rhombus is if its diagonals are perpendicular. To prove this using coordinate geometry you find the slope of the diagonal to see if they are perpendicular or the negative inverse.

Example: Is ABCD a rhombus?

A(-2,-1) B(-1,3) C(3,2) D(2,-2)

You can either prove its a rhombus by using slope formula to prove that the diagonals are perpendicular or by using distance formula to prove that it has 4 congruent sides.

For slope, find the slope of diagonals AC and BD to see if they are perpendicular to each other.

For distance, find the distance of each side, AB, BC, CD, and DA to see if they are congruent.

The answer is yes.

Square?

To prove that a shape is a square using coordinate geometry you need to prove one characteristic of a rectangle and one characteristic of a rhombus.

The next blogger will be Matt Newton, hurray!