Write a definition for dilation in math terms
3 answers
Dilation in math refers to the transformation of a geometric figure that either enlarges or reduces its size, while preserving its shape. This transformation is achieved by multiplying or dividing the coordinates of each point in the figure by a scale factor, which determines the degree of enlargement or reduction. Dilation can occur with respect to a center point or a fixed point, and the scale factor can be greater than 1 for enlargement or between 0 and 1 for reduction.
now explain dilation in a math problem
Sure! Let's consider a dilation of a triangle with a scale factor of 2 centered at the origin (0,0).
First, let's define the triangle ABC with coordinates A(2,4), B(4,2), and C(3,1).
To dilate this triangle by a scale factor of 2, we multiply the coordinates of each point by 2.
The new coordinates of the dilated triangle A'B'C' will be:
A'(2*2, 4*2) = A'(4, 8)
B'(4*2, 2*2) = B'(8, 4)
C'(3*2, 1*2) = C'(6, 2)
So, the dilated triangle with a scale factor of 2 centered at the origin is A'(4, 8), B'(8, 4), and C'(6, 2). This means that each point of the original triangle has been enlarged by a factor of 2 while maintaining the same shape and orientation relative to the center of dilation.
First, let's define the triangle ABC with coordinates A(2,4), B(4,2), and C(3,1).
To dilate this triangle by a scale factor of 2, we multiply the coordinates of each point by 2.
The new coordinates of the dilated triangle A'B'C' will be:
A'(2*2, 4*2) = A'(4, 8)
B'(4*2, 2*2) = B'(8, 4)
C'(3*2, 1*2) = C'(6, 2)
So, the dilated triangle with a scale factor of 2 centered at the origin is A'(4, 8), B'(8, 4), and C'(6, 2). This means that each point of the original triangle has been enlarged by a factor of 2 while maintaining the same shape and orientation relative to the center of dilation.