The coordinate plane is a two-dimensional plane formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. The point where the x-axis and y-axis intersect is called the origin, denoted as (0, 0).

The coordinate plane is divided into four regions called quadrants. The quadrants are labeled using Roman numerals in a counterclockwise direction starting from the top right quadrant.

- Quadrant I: The top right quadrant where both x and y-coordinates are positive.
- Quadrant II: The top left quadrant where x-coordinate is negative and y-coordinate is positive.
- Quadrant III: The bottom left quadrant where both x and y-coordinates are negative.
- Quadrant IV: The bottom right quadrant where x-coordinate is positive and y-coordinate is negative.

In the coordinate plane, a point is represented by an ordered pair (x, y), where x is the horizontal distance from the y-axis (positive to the right, negative to the left) and y is the vertical distance from the x-axis (positive upwards, negative downwards).

The distance between two points in the coordinate plane can be found using the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

To graph a point on the coordinate plane, start at the origin and move along the x-axis and then up or down along the y-axis to the point indicated by the ordered pair.

- What are the two axes that form the coordinate plane?
- What is the point of intersection of the x-axis and y-axis called?
- How are the quadrants labeled in the coordinate plane?
- What is an ordered pair and how is it represented on the coordinate plane?
- State the distance formula and explain its components.
- State the midpoint formula and explain its components.
- How do you graph a point on the coordinate plane?

These questions and concepts will help you understand and master the topic of the coordinate plane. Good luck with your studies!

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.