Understanding Rhombus through Coordinate Geometry

What is the first step in proving that a quadrilateral is a rhombus using coordinate geometry?

• Calculate the area of the quadrilateral

• Plot the points and find the intersection of the diagonals

• Check if all sides are equal

• Measure the angles of the quadrilateral

What property of parallelograms is used to prove that a quadrilateral is a parallelogram?

• All sides are equal

• Diagonals are perpendicular

• Diagonals bisect each other

• Opposite angles are equal

What is the significance of the midpoint in proving a quadrilateral is a parallelogram?

• It confirms the quadrilateral is a square

• It indicates the diagonals bisect each other

• It proves the diagonals are equal

• It shows the quadrilateral is a rectangle

What does the symbol with three dots represent in mathematical proofs?

• Moreover

• Because

• Therefore

• However

How do you prove that two lines are perpendicular using their slopes?

• Their slopes add up to zero

• Their slopes are positive reciprocals

• Their slopes are negative reciprocals

• Their slopes are equal

What is the slope of a line if the difference in y-values is -2 and the difference in x-values is -4?

• 2

• -1/2

• -2

• 1/2

What conclusion can be drawn if the diagonals of a parallelogram are perpendicular?

• The parallelogram is a trapezoid

• The parallelogram is a rhombus

• The parallelogram is a square

• The parallelogram is a rectangle

What alternative method can be used to prove a quadrilateral is a rhombus?

• Show that the diagonals are equal

• Show that all sides are equal

• Show that all angles are right angles

• Show that the area is maximum

What is the length of each side of the rhombus if counted vertically?

• 3 units

• 4 units

• 5 units

• 6 units

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