Math Problem Statement

Ch+7.1+HW+WS+.pdf

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solve these questions please

Solution

Let's go over the problems in your worksheet step by step. These problems involve applying a dilation transformation, where the figure is enlarged or reduced by a specific scale factor relative to the origin.

1. Dilation of 1.5 about the origin

You will multiply the coordinates of each vertex by the dilation factor 1.5.

For example, if a vertex is at (x,y)(x, y), the new coordinates after dilation will be (1.5x,1.5y)(1.5x, 1.5y).

2. Dilation of 52\frac{5}{2} about the origin

Multiply each vertex’s coordinates by 52\frac{5}{2} or 2.5.

3. Dilation of 12\frac{1}{2} about the origin

Multiply each vertex’s coordinates by 12\frac{1}{2} or 0.5.

4. Dilation of 0.25 about the origin

Multiply each vertex’s coordinates by 0.25.

5. Dilation of 2 about the origin

Multiply each vertex’s coordinates by 2.

6. Dilation of 2.5 about the origin

Multiply each vertex’s coordinates by 2.5.


For the transformations below, let's find the new coordinates of the vertices.

11. Dilation of 2.5 about the origin

Vertices: I(-2, -1), J(-2, 2), K(2, 1)

  • I=2.5×(2,1)=(5,2.5)I' = 2.5 \times (-2, -1) = (-5, -2.5)
  • J=2.5×(2,2)=(5,5)J' = 2.5 \times (-2, 2) = (-5, 5)
  • K=2.5×(2,1)=(5,2.5)K' = 2.5 \times (2, 1) = (5, 2.5)

12. Dilation of 2 about the origin

Vertices: T(-1, -1), U(0, 1), V(1, 0), W(1, -1)

  • T=2×(1,1)=(2,2)T' = 2 \times (-1, -1) = (-2, -2)
  • U=2×(0,1)=(0,2)U' = 2 \times (0, 1) = (0, 2)
  • V=2×(1,0)=(2,0)V' = 2 \times (1, 0) = (2, 0)
  • W=2×(1,1)=(2,2)W' = 2 \times (1, -1) = (2, -2)

13. Dilation of 14\frac{1}{4} about the origin

Vertices: Y(-2, 0), X(2, 2), W(1, -2)

  • Y=14×(2,0)=(0.5,0)Y' = \frac{1}{4} \times (-2, 0) = (-0.5, 0)
  • X=14×(2,2)=(0.5,0.5)X' = \frac{1}{4} \times (2, 2) = (0.5, 0.5)
  • W=14×(1,2)=(0.25,0.5)W' = \frac{1}{4} \times (1, -2) = (0.25, -0.5)

14. Dilation of 5 about the origin

Vertices: Y(1, -1), X(0, 1), W(1, 1)

  • Y=5×(1,1)=(5,5)Y' = 5 \times (1, -1) = (5, -5)
  • X=5×(0,1)=(0,5)X' = 5 \times (0, 1) = (0, 5)
  • W=5×(1,1)=(5,5)W' = 5 \times (1, 1) = (5, 5)

Would you like more details on any specific question? Here are some relative questions:

  1. How do you determine the scale factor for dilation transformations?
  2. How do you handle negative coordinates in dilations?
  3. What is the general effect of a dilation with a factor greater than 1 versus less than 1?
  4. How can you graphically represent dilation transformations?
  5. What are the differences between dilation and other transformations like translation or rotation?

Tip: Always double-check your new coordinates after a dilation by comparing the distance from the origin; it should increase or decrease according to the scale factor!

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Math Problem Analysis

Mathematical Concepts

Dilation Transformations
Coordinate Geometry

Formulas

New Coordinates = Scale Factor × Original Coordinates

Theorems

Dilation Theorem: Dilation multiplies the distance of every point from the origin by the same factor.

Suitable Grade Level

Grades 7-9