Distance and Reflections in the Coordinate Plane Flashcard

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 four quadrants of the coordinate plane?

Back

Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), Quadrant IV (x > 0, y < 0).

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 to get (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 to get (-x, y).

Front

What is the distance formula in 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

If point M is at (-3, -5), what is its reflection across the x-axis?

Back

The reflection of point M (-3, -5) across the x-axis is (-3, 5).

Front

In which quadrant is the point (3, -3)?

Back

Point (3, -3) is located in Quadrant IV.

Front

What happens to the coordinates of a point when it is reflected over the y-axis?

Back

The x-coordinate changes sign, while the y-coordinate remains the same.

Front

How far is the point (0, 0) from the point (3, -4)?

Back

Using the distance formula, the distance is 5 units.

Front

What is the reflection of point G in Quadrant IV across the x-axis?

Back

The reflection of point G in Quadrant IV across the x-axis will be in Quadrant III.