Question

In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.

Answer 1

From (0, 0), the points A and D are at (-1, -1) and (2, -1) respectively.

Since the scale factor is 2, every point will be moved twice a distance in both directions. (x and y).

So, multiplying both coordinates by 2, we will get the dilated points.

Hence, A' will be at (2 × (-1), 2 × (-1)) = (-2, -2)

D' will be at (2 × 2, 2 × (-1)) = (4, -2).

Answer 2

bnThe image vertices of A and D for dilation with center $\left( {0,0} \right)$ and scale factor of 2 are $\boxed{\left( { - 2, - 2} \right)}$ and $\boxed{\left( { 4, - 2} \right)}.$

Further explanation:

The rule of transformation of the coordinates can be expressed as follows,

$\boxed{\left( {x,y} \right) \to \left( {kx,ky} \right)}$

Here, k represents the scale factor.

Given:

The scale factor of images vertices is 2.

The image vertices for dilation with center $\left( {0,0} \right).$

Explanation:

The coordinate of vertices are $A = \left( { - 1,- 1} \right)$ and $D = \left( { 2,- 1} \right).$

The scale factor is 2.

The coordinate of image vertex of A can be calculated as,

$A\left( { - 1, - 1} \right) \to A'\left( {2 \times - 1,2 \times - 1} \right) = A'\left( { - 2, - 2} \right)$

The coordinate of image vertex of D can be calculated as,

$D\left( {2, - 1} \right) \to D'\left( {2 \times 2,2 \times - 1} \right) = D'\left( {4, - 2} \right)$

The image vertices of A and D for dilation with center \left( {0,0} \right) and scale factor of 2 are $\boxed{\left( { - 2, - 2} \right)}$ and $\boxed{\left({ 4, - 2}\right)}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: image vertices, dilation, center, scale factor, four, coordinates, x-coordinates, y-coordinate, transformation rule,