apply the transformation m to the triangle with the given vertices. name the coordinates of the image points. identify and describe the transformation
m: (x, y) -> (1.5x, 1.5y)
l(-1, 4), m(-4, 4), n(-4, 3)
b
a
b
c
b
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To apply the transformation m to the triangle with the given vertices, we will apply the transformation m to each vertex of the triangle.
Given triangle vertices:
L(-1, 4)
M(-4, 4)
N(-4, 3)
To apply the transformation m, we substitute the x and y coordinates of each vertex into the transformation rule:
For L(-1, 4):
m(L) = (1.5(-1), 1.5(4))
= (-1.5, 6)
The image point of vertex L under the transformation m is (-1.5, 6).
For M(-4, 4):
m(M) = (1.5(-4), 1.5(4))
= (-6, 6)
The image point of vertex M under the transformation m is (-6, 6).
For N(-4, 3):
m(N) = (1.5(-4), 1.5(3))
= (-6, 4.5)
The image point of vertex N under the transformation m is (-6, 4.5).
The transformation m: (x, y) -> (1.5x, 1.5y) is a dilation with a scale factor of 1.5 in both the x and y directions. This means that the image of each point is 1.5 times the distance from the origin in each direction. The triangle is scaled up by a factor of 1.5 in both the x and y directions.
To apply the transformation m to the triangle with the given vertices, we need to apply the transformation to each vertex individually. The transformation m: (x, y) -> (1.5x, 1.5y) scales the coordinates of each point by a factor of 1.5 in both the x and y directions.
Given the vertices of the triangle as l(-1, 4), m(-4, 4), and n(-4, 3), we can now apply the transformation m to each of these points to find the coordinates of the image points.
For the point l(-1, 4):
The transformed x-coordinate will be 1.5 times the original x-coordinate: 1.5 * (-1) = -1.5
The transformed y-coordinate will be 1.5 times the original y-coordinate: 1.5 * 4 = 6
So the image point of l under the transformation m is (-1.5, 6).
For the point m(-4, 4):
The transformed x-coordinate will be 1.5 times the original x-coordinate: 1.5 * (-4) = -6
The transformed y-coordinate will be 1.5 times the original y-coordinate: 1.5 * 4 = 6
So the image point of m under the transformation m is (-6, 6).
For the point n(-4, 3):
The transformed x-coordinate will be 1.5 times the original x-coordinate: 1.5 * (-4) = -6
The transformed y-coordinate will be 1.5 times the original y-coordinate: 1.5 * 3 = 4.5
So the image point of n under the transformation m is (-6, 4.5).
The transformation m: (x, y) -> (1.5x, 1.5y) is a dilation transformation with a scale factor of 1.5 in both the x and y directions. It enlarges the triangle by a factor of 1.5.