Geometry Distance and Area on Coordinate Plane

Front

What is the distance formula for two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

What is the Pythagorean Theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.

Front

How do you find the distance between two points on the same horizontal line?

Back

The distance is the absolute difference of their x-coordinates.

Front

How do you find the distance between two points on the same vertical line?

Back

The distance is the absolute difference of their y-coordinates.

Front

What are the coordinates of the midpoint between two points (x1, y1) and (x2, y2)?

Back

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Front

What is the area of a rectangle on the coordinate plane?

Back

Area = length × width, where length and width are the distances between the x and y coordinates.

Front

What is the formula for the area of a triangle given its base and height?

Back

Area = (1/2) × base × height.

Front

What is the definition of a right triangle?

Back

A triangle with one angle measuring 90 degrees.

Front

How can you determine if a triangle is a right triangle using coordinates?

Back

Check if the squares of the lengths of the two shorter sides add up to the square of the longest side.

Front

What is the significance of the x-axis and y-axis in the coordinate plane?

Back

They are the horizontal and vertical lines that define the plane and help locate points.