G 4.7 Coordinate Proofs

Front

What is a coordinate proof?

Back

A coordinate proof is a method of proving geometric theorems using a coordinate system, typically by placing geometric figures on a coordinate plane and using algebra to demonstrate relationships.

Front

What does the point E represent in a coordinate proof?

Back

Point E represents a variable point in the coordinate plane, often used to express the height or other dimensions of a geometric figure.

Front

If a triangle has vertices at (0, 0), (a, 0), and (0, b), what is the height of the triangle?

Back

The height of the triangle is b, which is the y-coordinate of the vertex opposite the base.

Front

What is the significance of using variables like x and y in coordinate proofs?

Back

Variables like x and y are used to represent unknown coordinates of points, allowing for generalization and flexibility in proofs.

Front

How do you determine the coordinates of point C if it is on the line y = q?

Back

The coordinates of point C can be expressed as (x, q), where x can be any value along the line.

Front

What does the notation (a, a) signify in a coordinate proof?

Back

The notation (a, a) signifies a point where the x-coordinate and y-coordinate are equal, often representing a diagonal line in the coordinate plane.

Front

In a coordinate proof, how can you express the coordinates of point M if it lies on the y-axis?

Back

If point M lies on the y-axis, its coordinates can be expressed as (0, y), where y is the distance from the origin.

Front

What is the purpose of using a coordinate system in geometry?

Back

A coordinate system provides a framework for locating points, lines, and shapes in a plane, making it easier to analyze and prove geometric relationships.

Front

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

Back

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

Front

How can you find the midpoint of a line segment between points (x1, y1) and (x2, y2)?

Back

The midpoint can be found using the formula: M = ((x1 + x2)/2, (y1 + y2)/2).