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Name Date Dilations and Parallel Lines Stepsister Lesson Line has the equation y 2x + 2. Write the equation of the image of after dilation with a scale factor of 4, centered at the origin. Write your

How to fill out dilations and parallel lines

How to fill out dilations and parallel lines:

1. Start by understanding the concept of dilations. Dilations involve enlarging or shrinking a geometric figure while maintaining proportional relationships between the corresponding sides.
2. Identify the center of dilation, which is the fixed point from which the dilation occurs. This point will be used as a reference to determine the scale factor.
3. Determine the scale factor, which indicates how much the figure will be enlarged or shrunk. A scale factor greater than 1 will result in an enlargement, while a scale factor between 0 and 1 will result in a reduction.
4. Multiply the coordinates of each point in the original figure by the scale factor to find the corresponding coordinates in the dilated figure.
5. Connect the corresponding points in the dilated figure to complete the dilated shape.
6. To work with parallel lines, start by identifying two or more lines that never intersect, appearing to be side by side or equidistant from each other.
7. Understand the concept of parallel lines being equidistant from each other. This means that the distance between any two points on one line is equal to the distance between the corresponding points on the other line.
8. Use a ruler and measure the distance between any two corresponding points on the parallel lines to verify their equidistance.
9. Recognize the properties and geometric relationships that parallel lines possess, including the ability to create congruent angles when intersected by a transversal line.
10. Solve problems involving parallel lines by utilizing the properties and theorems associated with them.

Who needs dilations and parallel lines?

1. Architects and engineers often use dilations to create scaled drawings of buildings or structures. This helps them visualize and plan without the need for building the entire structure.
2. Artists and designers may use dilations to resize images or objects in their artwork, maintaining proper proportions.
3. Students studying geometry or mathematics need to understand dilations and parallel lines to solve problems and analyze geometric figures accurately.
4. Surveyors and cartographers utilize parallel lines to create accurate maps and layouts, ensuring that lines representing roads, boundaries, or land features do not intersect unless intentional.
5. Mathematicians and researchers may need to analyze the properties, relationships, and applications of dilations and parallel lines for various mathematical theories or research projects.

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What is dilations and parallel lines?

Dilations involve resizing figures on a coordinate plane by a scale factor. Parallel lines are lines in a plane which do not meet.

Who is required to file dilations and parallel lines?

Students studying geometry or mathematics may be required to work with dilations and parallel lines.

How to fill out dilations and parallel lines?

Dilations can be filled out by applying the scale factor to the x and y coordinates of the original figure. Parallel lines can be identified by their equal slopes.

What is the purpose of dilations and parallel lines?

The purpose of dilations is to resize figures proportionally. Parallel lines help in identifying relationships between angles and shapes.

What information must be reported on dilations and parallel lines?

On dilations, the scale factor and coordinates of the original figure must be reported. On parallel lines, the equations of the lines and their slopes must be provided.