Math  /  Geometry

Question4. Dilate quadrilateral ABCDA B C D using center DD and scale factor 2 . (From Unit 3, Lesson 2.)
5. Dilate Figure GG using center BB and scale factor 3 .

Studdy Solution

STEP 1

1. Quadrilateral ABCDABCD is defined on a coordinate grid.
2. The dilation is performed with respect to a center point, which is one of the vertices of the quadrilateral.
3. The scale factor indicates how much larger or smaller the dilated figure will be compared to the original.

STEP 2

1. Understand the concept of dilation.
2. Apply dilation to quadrilateral ABCDABCD using center DD and scale factor 2.
3. Apply dilation to Figure GG using center BB and scale factor 3.

STEP 3

Understand the concept of dilation:
- Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. - The dilation is defined by a center point and a scale factor. - If the scale factor is greater than 1, the image is an enlargement; if it is between 0 and 1, the image is a reduction.

STEP 4

Apply dilation to quadrilateral ABCDABCD using center DD and scale factor 2:
1. Identify the coordinates of points AA, BB, CC, and DD.
2. For each point PP (where PP is AA, BB, or CC), calculate the dilated point PP' using the formula: P' = D + 2(P - D) \] This means for each coordinate \( (x, y) \) of point \( P \), calculate: x' = x_D + 2(x - x_D) \] $ y' = y_D + 2(y - y_D) \]
3. Plot the new points \(A'\), \(B'\), and \(C'\) on the grid to form the dilated quadrilateral \(A'B'C'D\).

STEP 5

Apply dilation to Figure GG using center BB and scale factor 3:
1. Identify the coordinates of the points that make up Figure GG.
2. For each point PP in Figure GG, calculate the dilated point PP' using the formula: P' = B + 3(P - B) \] This means for each coordinate \( (x, y) \) of point \( P \), calculate: x' = x_B + 3(x - x_B) \] $ y' = y_B + 3(y - y_B) \]
3. Plot the new points to form the dilated Figure \(G'\).

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