Classifying a quadrilateral on the coordinate plane | Analytic geometry | Geometry | Khan Academy

TL;DR

The quadrilateral ABCD cannot be classified as any specific shape due to the lack of parallel sides.

Transcript

Classify quadrilateral ABCD. Choose the option that best suits the quadrilateral. We're going to pick whether it's a square, rhombus, rectangle, parallelogram, trapezoid, none of the above. And I'm assuming we're going to pick the most specific one possible, because obviously all squares are rhombuses, or rhombi, I guess you'd say. Not all rhombi a... Read More

Key Insights

• ❓ Quadrilateral ABCD has the coordinates A(1, 6), B(-5, 2), C(-7, 8), and D(2, 11).
• 🙃 None of the sides of ABCD are parallel to each other.
• ❎ Quadrilateral ABCD cannot be classified as a specific shape, such as a square, rhombus, rectangle, parallelogram, or trapezoid.
• 🙃 Classifying quadrilaterals requires determining if any of their sides are parallel.
• 🫥 Slope can be used to determine if lines are parallel or not.
• 🙃 The slope of side AB is 2/3, and the slope of side CD is 1/3, indicating that these sides are not parallel.
• 🙃 A parallelogram requires two pairs of parallel sides, while a trapezoid requires only one pair of parallel sides.

Questions & Answers

Q: How can we classify quadrilateral ABCD based on its given coordinates?

We can classify the quadrilateral based on whether its sides are parallel to each other. In this case, none of the sides are parallel, so it cannot be classified as any specific shape.

Q: What are the coordinates of the four points of the quadrilateral?

The coordinates are A(1, 6), B(-5, 2), C(-7, 8), and D(2, 11).

Q: Are any of the sides of quadrilateral ABCD parallel?

No, none of the sides are parallel to each other.

Q: Can quadrilateral ABCD be classified as a rectangle?

No, because a rectangle must have two pairs of parallel sides, and quadrilateral ABCD does not have any parallel sides.

Summary & Key Takeaways

• The coordinates of the four points of quadrilateral ABCD are given: A(1, 6), B(-5, 2), C(-7, 8), and D(2, 11).

• None of the sides of the quadrilateral are parallel to each other, making it impossible to classify it as a specific shape.

• Therefore, the quadrilateral ABCD cannot be classified as a square, rhombus, rectangle, parallelogram, or trapezoid.