Describe the effect of the dilation of the angle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0). Angle A'(5,4), B'(-2,2), C'(2,-3).
Dilation is a transformation that uniformly enlarges or reduces an object by a certain scale factor. In this case, we are dilating the angle ABC with a scale factor of 5 and a center of dilation at the origin (0,0).
To perform the dilation, we need to multiply the coordinates of each point by the scale factor. Let's calculate the new coordinates of the angle after dilation.
For point A:
x-coordinate of A' = scale factor * x-coordinate of A = 5 * 0 = 0
y-coordinate of A' = scale factor * y-coordinate of A = 5 * 4 = 20
Hence, the new coordinates of point A' after dilation are (0, 20).
For point B:
x-coordinate of B' = scale factor * x-coordinate of B = 5 * (-2) = -10
y-coordinate of B' = scale factor * y-coordinate of B = 5 * 2 = 10
Hence, the new coordinates of point B' after dilation are (-10, 10).
For point C:
x-coordinate of C' = scale factor * x-coordinate of C = 5 * 2 = 10
y-coordinate of C' = scale factor * y-coordinate of C = 5 * (-3) = -15
Hence, the new coordinates of point C' after dilation are (10, -15).
Therefore, after dilation with a scale factor of 5 and a center of dilation at the origin, the new coordinates of the angle ABC are A'(0, 20), B'(-10, 10), and C'(10, -15).
To describe the effect of the dilation of angle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0), let's go through the steps:
1. Find the coordinates of the original points A, B, and C.
- A(5,4)
- B(-2,2)
- C(2,-3)
2. Apply the dilation to each of the original points.
- Apply the scale factor of 5 to the x and y coordinates:
- A' = (5 * 5, 4 * 5) = (25, 20)
- B' = (-2 * 5, 2 * 5) = (-10, 10)
- C' = (2 * 5, -3 * 5) = (10, -15)
3. Interpret the result.
- After the dilation, the new coordinates of the points are:
- A': (25, 20)
- B': (-10, 10)
- C': (10, -15)
- The effect of the dilation is that all the points are moved away from the origin, and the distance between the points and the origin is increased by a factor of 5.
- The angle ABC is also affected by the dilation. The angle becomes wider as the points move away from the origin, but the shape of the angle remains the same.
- In this case, the point A' is moved to (25, 20), the point B' is moved to (-10, 10), and the point C' is moved to (10, -15), effectively dilating the angle ABC with a scale factor of 5 and a center of dilation at the origin.