Graphing, Reflections, Distance on Coordinate Plane

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

A pair of numbers (x, y) that define the position of a point on the coordinate plane, where 'x' represents the horizontal position and 'y' represents the vertical position.

Front

How do you reflect a point across the x-axis?

Back

To reflect a point (x, y) across the x-axis, change the sign of the y-coordinate, resulting in the new point (x, -y).

Front

How do you reflect a point across the y-axis?

Back

To reflect a point (x, y) across the y-axis, change the sign of the x-coordinate, resulting in the new point (-x, y).

Front

What is the reflection of the point (4, 3) over the x-axis?

Back

(4, -3) - The y-coordinate changes sign.

Front

What is the reflection of the point (-2, -5) over the y-axis?

Back

(2, -5) - The x-coordinate changes sign.

Front

What is a reflection in geometry?

Back

A transformation that produces a mirror image of a shape or point across a line (axis), creating a symmetrical figure.

Front

What is the distance formula on the coordinate plane?

Back

The distance between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

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

Front

What does it mean for two points to be symmetric with respect to the x-axis?

Back

Two points (x, y) and (x, -y) are symmetric with respect to the x-axis if they are reflections of each other across the x-axis.