The Coordinate Plane, Distance, & Reflections

Front

What are the four quadrants of the coordinate plane?

Back

1st Quadrant: (+, +), 2nd Quadrant: (-, +), 3rd Quadrant: (-, -), 4th Quadrant: (+, -)

Front

How do you determine the quadrant of a point (x, y)?

Back

Check the signs of x and y: If x > 0 and y > 0, it's in the 1st Quadrant; if x < 0 and y > 0, it's in the 2nd Quadrant; if x < 0 and y < 0, it's in the 3rd Quadrant; if x > 0 and y < 0, it's in the 4th Quadrant.

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

What is the distance between the points (a, b) and (a, c) on a horizontal line?

Back

Distance = |b - c|, since the x-coordinates are the same.

Front

What is the distance between the points (a, b) and (c, b) on a vertical line?

Back

Distance = |a - c|, since the y-coordinates are the same.

Front

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

Back

The y-axis is the vertical line where x = 0, and it separates the 1st and 2nd quadrants from the 3rd and 4th quadrants.

Front

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

Back

The x-axis is the horizontal line where y = 0, and it separates the upper quadrants (1st and 2nd) from the lower quadrants (3rd and 4th).

Front

How do you identify a point on the y-axis?

Back

A point is on the y-axis if its x-coordinate is 0, e.g., (0, y).

Front

How do you identify a point on the x-axis?

Back

A point is on the x-axis if its y-coordinate is 0, e.g., (x, 0).

Front

What is the relationship between the coordinates of a point in the 1st quadrant?

Back

Both x and y coordinates are positive.