A triangle has vertices X(2,2) ,Y(4,2)and Z(3,4).The triangle is enlarged by a scale factor 2 through the origin.What are the coordinates of the image?
(2,2) ---> (-4,-4)
(4,2) ---> (-8,-4)
(3,4) ---> (-6,-8)
To find the coordinates of the image after enlarging the triangle by a scale factor of 2 through the origin, we can use the concept of dilation.
Dilation is a transformation that enlarges or reduces the size of a figure without changing its shape. When dilating a figure through the origin, each coordinate of the original figure is multiplied by the scale factor. In this case, the scale factor is 2.
Let's calculate the new coordinates of the triangle:
For point X(2, 2):
- Multiply the x-coordinate by the scale factor 2: 2 * 2 = 4
- Multiply the y-coordinate by the scale factor 2: 2 * 2 = 4
So, the image of X is X'(4, 4).
For point Y(4, 2):
- Multiply the x-coordinate by the scale factor 2: 4 * 2 = 8
- Multiply the y-coordinate by the scale factor 2: 2 * 2 = 4
So, the image of Y is Y'(8, 4).
For point Z(3, 4):
- Multiply the x-coordinate by the scale factor 2: 3 * 2 = 6
- Multiply the y-coordinate by the scale factor 2: 4 * 2 = 8
So, the image of Z is Z'(6, 8).
Therefore, the coordinates of the image triangle after enlarging by a scale factor of 2 through the origin are X'(4, 4), Y'(8, 4), and Z'(6, 8).