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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.6.G.A.3

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.

Tags

CCSS.6.G.A.3

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.

Tags

CCSS.5.G.A.1

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.

Tags

CCSS.5.G.A.1

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.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.5.G.A.1

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).

Tags

CCSS.HSG.GPE.B.7

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).

Tags

CCSS.HSG.GPE.B.6