1. Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A (3,7) and B (4,9).
To find the coordinates A' and B' after dilation, we need to apply the scale factor of 2 to the x and y coordinates of points A and B, centered at the origin (0, 0).
For point A (3, 7):
- Multiply the x-coordinate by the scale factor 2: 3 * 2 = 6
- Multiply the y-coordinate by the scale factor 2: 7 * 2 = 14
Therefore, the coordinates of A' after dilation are (6, 14).
For point B (4, 9):
- Multiply the x-coordinate by the scale factor 2: 4 * 2 = 8
- Multiply the y-coordinate by the scale factor 2: 9 * 2 = 18
Therefore, the coordinates of B' after dilation are (8, 18).
In summary:
A' = (6, 14)
B' = (8, 18)
Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 1/3, centered at the origin where the endpoints are A (-6,3) and B (-12,9).
To find the coordinates A' and B' after dilation, we need to apply the scale factor of 1/3 to the x and y coordinates of points A and B, centered at the origin (0, 0).
For point A (-6, 3):
- Multiply the x-coordinate by the scale factor 1/3: -6 * 1/3 = -2
- Multiply the y-coordinate by the scale factor 1/3: 3 * 1/3 = 1
Therefore, the coordinates of A' after dilation are (-2, 1).
For point B (-12, 9):
- Multiply the x-coordinate by the scale factor 1/3: -12 * 1/3 = -4
- Multiply the y-coordinate by the scale factor 1/3: 9 * 1/3 = 3
Therefore, the coordinates of B' after dilation are (-4, 3).
In summary:
A' = (-2, 1)
B' = (-4, 3)
3. Line AB contains point A (-4,1) and point B (-1,3). Find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin.
To find the coordinates A' and B' after a dilation with a scale factor of 2 and a center point of dilation at the origin, we need to multiply the x and y coordinates of points A and B by the scale factor 2.
For point A (-4, 1):
- Multiply the x-coordinate by the scale factor 2: -4 * 2 = -8
- Multiply the y-coordinate by the scale factor 2: 1 * 2 = 2
Therefore, the coordinates of A' after dilation are (-8, 2).
For point B (-1, 3):
- Multiply the x-coordinate by the scale factor 2: -1 * 2 = -2
- Multiply the y-coordinate by the scale factor 2: 3 * 2 = 6
Therefore, the coordinates of B' after dilation are (-2, 6).
In summary:
A' = (-8, 2)
B' = (-2, 6)
Line AB contains point A (1,2) and point B (-2,-1). Find the coordinates of A' and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin.
To find the coordinates A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we need to multiply the x and y coordinates of points A and B by the scale factor 5.
For point A (1, 2):
- Multiply the x-coordinate by the scale factor 5: 1 * 5 = 5
- Multiply the y-coordinate by the scale factor 5: 2 * 5 = 10
Therefore, the coordinates of A' after dilation are (5, 10).
For point B (-2, -1):
- Multiply the x-coordinate by the scale factor 5: -2 * 5 = -10
- Multiply the y-coordinate by the scale factor 5: -1 * 5 = -5
Therefore, the coordinates of B' after dilation are (-10, -5).
In summary:
A' = (5, 10)
B' = (-10, -5)
5. Describe the dilation of triangle ABC, with a scale factor of 5 and a center point of dilation at the origin (0,0).
When triangle ABC is dilated with a scale factor of 5 and a center point of dilation at the origin (0, 0), the resulting triangle will have each of its sides extended or contracted by a factor of 5 and its angles will remain the same.
Specifically, suppose triangle ABC has vertices A(x1, y1), B(x2, y2), and C(x3, y3).
After dilation:
- The distance between each pair of corresponding vertices will be multiplied by the scale factor 5. For example, the distance between A' and B' will be 5 times larger than the distance between A and B.
- The position of each vertex will be adjusted according to the dilation. For example, if the x-coordinate of vertex A is x1, after dilation the x-coordinate of A' will be 5 * x1.
- The shape of the triangle will be preserved, but it will be larger or smaller depending on the scale factor.
Overall, the dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin will result in a larger or smaller triangle with the same angles as the original triangle.
5. Describe the dilation of triangle ABC, with a scale factor of 5 and a center point of dilation at the origin (0,0).
A. Triangle A'B'C' is 5 times as large as triangle ABC and is 5 times closer to the center point of dilation.
B. Triangle A'B'C' is 5 times as smaller than triangle ABC and is 5 times closer to the center point of dilation.
C. Triangle A'B'C' is 5 times as smaller than triangle ABC and is 5 times as far from the center point of dilation.
D. Triangle A'B'C' is 5 times as large as triangle ABC and is 5 times as far from the center point of dilation.