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).
bnThe image vertices of A and D for dilation with center [tex]\left( {0,0} \right)[/tex] and scale factor of 2 are [tex]\boxed{\left( { - 2, - 2} \right)}[/tex] and [tex]\boxed{\left( { 4, - 2} \right)}.[/tex]
Further explanation:
The rule of transformation of the coordinates can be expressed as follows,
[tex]\boxed{\left( {x,y} \right) \to \left( {kx,ky} \right)}[/tex]
Here, k represents the scale factor.
Given:
The scale factor of images vertices is 2.
The image vertices for dilation with center [tex]\left( {0,0} \right).[/tex]
Explanation:
The coordinate of vertices are [tex]A = \left( { - 1,- 1} \right)[/tex] and [tex]D = \left( { 2,- 1} \right).[/tex]
The scale factor is 2.
The coordinate of image vertex of A can be calculated as,
[tex]A\left( { - 1, - 1} \right) \to A'\left( {2 \times - 1,2 \times - 1} \right) = A'\left( { - 2, - 2} \right)[/tex]
The coordinate of image vertex of D can be calculated as,
[tex]D\left( {2, - 1} \right) \to D'\left( {2 \times 2,2 \times - 1} \right) = D'\left( {4, - 2} \right)[/tex]
The image vertices of A and D for dilation with center \left( {0,0} \right) and scale factor of 2 are [tex]\boxed{\left( { - 2, - 2} \right)}[/tex] and [tex]\boxed{\left({ 4, - 2}\right)}.[/tex]
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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,
