Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
D:(x, y) -->(3x, 3y)
J(1, 4), K(6, 4), L(6, 1) and M(1, 1)
a
J'(12, 3), K'(12, 18), L'(3, 18), M'(3, 3)
b
J'(-3, -12), K'(-18, -12), L'(-18, -3), M'(-3, -3)
c
J'(3, 12), K'(18, 12), L'(6, 1), M'(1, 1)
d
J'(3, 12), K'(18, 12), L'(18, 3), M'(3, 3)
multiply each x value by 3
3 , 18 , 18 , 3
multiply each y value by 3
12, 12 , 3 , 3
(3,12) (18,12) (18,3) (3,3)
To apply the dilation D:(x, y) -->(3x, 3y) to the given polygon with vertices J(1, 4), K(6, 4), L(6, 1), and M(1, 1), we will substitute each coordinate into the dilation formula and calculate the new coordinates.
a) J'(12, 3), K'(12, 18), L'(3, 18), M'(3, 3)
To find J', we substitute the coordinates of J into the dilation formula:
J'(x, y) = (3x, 3y)
J'(1, 4) = (3 * 1, 3 * 4) = (3, 12)
To find K', we substitute the coordinates of K:
K'(x, y) = (3x, 3y)
K'(6, 4) = (3 * 6, 3 * 4) = (18, 12)
To find L', we substitute the coordinates of L:
L'(x, y) = (3x, 3y)
L'(6, 1) = (3 * 6, 3 * 1) = (18, 3)
To find M', we substitute the coordinates of M:
M'(x, y) = (3x, 3y)
M'(1, 1) = (3 * 1, 3 * 1) = (3, 3)
Therefore, the correct answer is a) J'(12, 3), K'(12, 18), L'(3, 18), M'(3, 3).
To apply the dilation D to the polygon with the given vertices, you will need to apply the given transformation rule to each vertex of the polygon.
The dilation rule given is D: (x, y) --> (3x, 3y). This means that to find the image of a point (x, y) after dilation, you need to multiply the x-coordinate by 3 and the y-coordinate by 3.
Let's apply this rule to each vertex of the given polygon:
1. Vertex J(1, 4):
Applying the dilation rule: (1, 4) --> (3*1, 3*4) --> (3, 12)
The image point J' is (3, 12).
2. Vertex K(6, 4):
Applying the dilation rule: (6, 4) --> (3*6, 3*4) --> (18, 12)
The image point K' is (18, 12).
3. Vertex L(6, 1):
Applying the dilation rule: (6, 1) --> (3*6, 3*1) --> (18, 3)
The image point L' is (18, 3).
4. Vertex M(1, 1):
Applying the dilation rule: (1, 1) --> (3*1, 3*1) --> (3, 3)
The image point M' is (3, 3).
Now let's check the options to see if any of them match the image points obtained:
a) J'(12, 3), K'(12, 18), L'(3, 18), M'(3, 3)
This option matches the image points obtained, so it is the correct answer.
b) J'(-3, -12), K'(-18, -12), L'(-18, -3), M'(-3, -3)
This option does not match the image points obtained.
c) J'(3, 12), K'(18, 12), L'(6, 1), M'(1, 1)
This option does not match the image points obtained.
d) J'(3, 12), K'(18, 12), L'(18, 3), M'(3, 3)
This option does not match the image points obtained.
Therefore, the correct answer is option a: J'(12, 3), K'(12, 18), L'(3, 18), M'(3, 3).