Exploring Coordinate Geometry Proofs

What formulas are primarily used to prove quadrilaterals in coordinate geometry?

• Area and Perimeter

• Midpoint and Distance

• Slope and Midpoint

• Slope and Distance

Which method can be used to show that both pairs of opposite sides of a parallelogram are parallel?

• Using the Slope Formula

• Using the Distance Formula

• Using the Area Formula

• Using the Midpoint Formula

What is the significance of diagonals having the same midpoint in a quadrilateral?

• They are equal in length

• They are parallel

• They bisect each other

• They are perpendicular

To prove a rectangle, what must be shown about one of its angles?

• It is 60°

• It is 90°

• It is 45°

• It is 120°

What is the relationship between the slopes of perpendicular lines?

• They are equal

• They are negative reciprocals

• They are positive reciprocals

• They are zero

What should you do if the grid is optional in a coordinate geometry proof?

• Ask the teacher

• Use it only if you have time

• Use it

• Ignore it

Why is it important to organize your work in coordinate geometry proofs?

• To use less paper

• To make it look neat

• To ensure the grader can follow your logic

• To save time

In the example, what is the first step to prove the quadrilateral is a rectangle?

• Calculate the area

• Find the slopes of opposite sides

• Measure the angles

• Find the midpoints

What should be included in the concluding statement of a proof?

• A specific statement tying all work together

• A list of formulas used

• A restatement of the problem

• A summary of the steps

What is the final step in proving the quadrilateral is a rectangle in the example?

• Measuring the sides

• Calculating the area

• Finding the midpoints

• Showing one right angle