1. Line Segment AB has endpoints A (-6,4) and B (-8,2). Find the coordinates of A' and B' after a dilation with a scale factor of 1/2, centered at the origin.
2. Determine the scale factor used in the dilation of line segment AB, centered at the origin. A (2,3) to B (4,1) and A' (6,9) to B' (12,3)
3. Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin. A' (-6,8) B' (4,-8) and A (-3,4) B (2,-4)
4. Triangle ABC has vertices point A (2,1) point B (4,3) and point C (-2,5). Find the coordinates of A', B', and C' after a dilation with a scale factor of 7 and a center point of dilation at the origin (0,0)
5. Triangle ABC has vertices point A (2,1) point B (-2,2) and point C (-3,-1). After dilation, triangle A'B'C' has vertices point A' (4,2) point B' (-4,4 and point C' (-6,-2). Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0,0).
1. To find the coordinates of A' and B' after a dilation with a scale factor of 1/2, centered at the origin, you can multiply each coordinate by the scale factor.
For point A (-6,4), the x-coordinate becomes -6 * (1/2) = -3 and the y-coordinate becomes 4 * (1/2) = 2. So, A' is (-3, 2).
For point B (-8,2), the x-coordinate becomes -8 * (1/2) = -4 and the y-coordinate becomes 2 * (1/2) = 1. So, B' is (-4, 1).
2. To determine the scale factor used in the dilation of line segment AB, centered at the origin, you can calculate the ratio of the lengths of the corresponding sides after dilation.
The length of AB is √[(4-2)^2 + (1-3)^2] = √[4 + 4] = √8.
The length of A'B' is √[(12-6)^2 + (3-9)^2] = √[36 + 36] = √72 = 6√2.
The scale factor is the ratio of the lengths of the corresponding sides: (6√2) / √8 = 3.
3. To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, you can calculate the ratio of the lengths of the corresponding sides after dilation.
The length of AB is √[(-3-2)^2 + (4-(-4))^2] = √[25 + 64] = √89.
The length of A'B' is √[(4-(-6))^2 + (2-(-8))^2] = √[100 + 100] = √200 = 10√2.
The scale factor is the ratio of the lengths of the corresponding sides: (10√2) / √89.
4. To find the coordinates of A', B', and C' after a dilation with a scale factor of 7 and a center point of dilation at the origin, you can multiply each coordinate by the scale factor.
For point A (2,1), the x-coordinate becomes 2 * 7 = 14 and the y-coordinate becomes 1 * 7 = 7. So, A' is (14, 7).
For point B (4,3), the x-coordinate becomes 4 * 7 = 28 and the y-coordinate becomes 3 * 7 = 21. So, B' is (28, 21).
For point C (-2,5), the x-coordinate becomes -2 * 7 = -14 and the y-coordinate becomes 5 * 7 = 35. So, C' is (-14, 35).
5. To determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin, you can calculate the ratio of the lengths of the corresponding sides after dilation.
The length of AB is √[(-2-2)^2 + (2-1)^2] = √[16 + 1] = √17.
The length of A'B' is √[(-4-4)^2 + (2-4)^2] = √[64 + 4] = √68 = 2√17.
The scale factor is the ratio of the lengths of the corresponding sides: (2√17) / √17 = 2.
To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, we can calculate the ratio of the distances from the origin to the corresponding points before and after dilation.
Before dilation:
For point A (-3, 4), the distance from the origin is √((-3)^2 + 4^2) = √(9 + 16) = √25 = 5.
For point B (2, -4), the distance from the origin is √(2^2 + (-4)^2) = √(4 + 16) = √20 = 2√5.
After dilation:
For point A' (-6, 8), the distance from the origin is √((-6)^2 + 8^2) = √(36 + 64) = √100 = 10.
For point B' (4, -8), the distance from the origin is √(4^2 + (-8)^2) = √(16 + 64) = √80 = 4√5.
Therefore, the scale factor used in the dilation of line AB is (distance after dilation) / (distance before dilation) = (4√5) / (2√5) = 4/2 = 2.
3 is wrong
wrong
Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin. A' (-6,8) B' (4,-8) and A (-3,4) B (2,-4)
Apologies for the mistake in my previous response.
To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, you can calculate the ratio of the lengths of the corresponding sides after dilation.
The length of AB is √[(-3-2)^2 + (4-(-4))^2] = √[25 + 64] = √89.
The length of A'B' is √[(4-(-6))^2 + (2-(-8))^2] = √[100 + 100] = √200 = 10√2.
The scale factor is the ratio of the lengths of the corresponding sides: (10√2) / √89 ≈ 2.83.
Apologies for the continued mistake.
To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, you can calculate the ratio of the lengths of the corresponding sides after dilation.
The length of AB is √[(4-2)^2 + (1-3)^2] = √[4 + 4] = √8.
The length of A'B' is √[(12-6)^2 + (3-9)^2] = √[36 + 36] = √72 = 6√2.
The scale factor is the ratio of the lengths of the corresponding sides: (6√2) / √8 = 6/√2 = 3√2.