The dilation does not pass through the center of dilation for both point A and point B.
To determine whether the dilation passes through the center of dilation, we need to compare the original points with their corresponding images after dilation. In this case, the original points are labeled A and B.
Looking at point A, its image after dilation is located at (-2, 4). Similarly, point B has an image at (3, 7) after dilation.
To find the center of dilation, we can calculate the midpoint of the line segment joining the original point and its image. Let's start with point A:
Midpoint of A = ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 )
= ( (-1 + -2) / 2, (0 + 4) / 2 )
= ( (-3) / 2, 4 / 2 )
= ( -1.5, 2 )
Next, let's find the midpoint of point B:
Midpoint of B = ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 )
= ( (3 + 3) / 2, (4 + 7) / 2 )
= ( 6 / 2, 11 / 2 )
= ( 3, 5.5 )
Now, we compare the midpoints with the original points:
- The midpoint of A (-1.5, 2) does not match the original point A (-1, 0). Therefore, the dilation does not pass through the center of dilation for point A.
- The midpoint of B (3, 5.5) does not match the original point B (2, 3). Hence, the dilation does not pass through the center of dilation for point B.
In conclusion, the dilation does not pass through the center of dilation for both point A and point B.