5.G.2 Coordinate Planes (Real-World Problems)

Front

What is a coordinate plane?

Back

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis). Each point on the plane is defined by an ordered pair of numbers (x, y).

Front

What does the ordered pair (x, y) represent?

Back

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

Front

How do you find the distance between two points on a coordinate plane?

Back

To find the distance between two points (x1, y1) and (x2, y2), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does it mean for points to be collinear?

Back

Points are collinear if they lie on the same straight line.

Front

How do you determine the slope of a line between two points?

Back

The slope (m) of a line between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the origin in a coordinate plane?

Back

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

Front

If a point is located at (3, 4), how many units is it from the origin?

Back

The distance from the origin to the point (3, 4) is 5 units, calculated using the distance formula: d = √(3² + 4²) = 5.

Front

What direction do you travel to go from (1, 2) to (4, 5)?

Back

To go from (1, 2) to (4, 5), you travel 3 units east and 3 units north.

Front

What is the significance of the x-axis and y-axis?

Back

The x-axis is the horizontal line on the coordinate plane, while the y-axis is the vertical line. They are used to define the position of points.

Front

How can you identify a point that lies on a line segment?

Back

A point lies on a line segment if its coordinates satisfy the linear equation formed by the endpoints of the segment.