G 4.7 Coordinate Proofs

Front

What is a coordinate proof?

Back

A coordinate proof is a method of proving geometric theorems using algebra and the coordinate plane.

Front

How do you represent a point in the coordinate plane?

Back

A point in the coordinate plane is represented as an ordered pair (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

Front

What is the significance of the x-coordinate in a point (x, 0)?

Back

The x-coordinate indicates the horizontal position of the point on the x-axis, while the y-coordinate of 0 means the point lies on the x-axis.

Front

What does the point (0, y) represent?

Back

The point (0, y) represents a point on the y-axis, where y is the vertical coordinate.

Front

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

Back

The midpoint M is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2).

Front

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

Back

The distance d is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the slope of a line through points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel in terms of slope?

Back

Two lines are parallel if they have the same slope.

Front

What does it mean for two lines to be perpendicular in terms of slope?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

How can you determine if a point lies on a line given by the equation y = mx + b?

Back

A point (x, y) lies on the line if substituting x into the equation yields the corresponding y value.