Coordinate Plane & Pythagorean Theorem

Front

What is the coordinate plane?

Back

A two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis), used to locate points using ordered pairs (x, y).

Front

What are the coordinates of a point?

Back

An ordered pair (x, y) that defines the position of a point on the coordinate plane, where 'x' is the horizontal distance from the origin and 'y' is the vertical distance.

Front

What is the Pythagorean Theorem?

Back

A mathematical principle stating that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the y-axis on the coordinate plane?

Back

The vertical line that runs up and down through the origin (0,0), representing all points where x = 0.

Front

What is the x-axis on the coordinate plane?

Back

The horizontal line that runs side to side through the origin (0,0), representing all points where y = 0.

Front

How do you identify a rectangle on the coordinate plane?

Back

A rectangle can be identified by having opposite sides that are equal in length and four right angles.

Front

What are the coordinates of the origin?

Back

The origin is the point (0, 0) where the x-axis and y-axis intersect.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because it does not have a change in x (the denominator in the slope formula is zero).