Line AB and line CD are parallel lines. Line AB contains the points A(-5,-5) and B(-3,-2), and line CD contains the points C (-7,-2) and D (-5,-1). Describe the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0).
A dilation is a transformation that resizes an object without changing its shape. In this case, the dilation has a scale factor of 3 and a center point at the origin (0,0).
To perform the dilation, we need to apply the scale factor of 3 to both the x-coordinates and y-coordinates of the points.
For point A(-5,-5), the x-coordinate becomes 3*(-5) = -15, and the y-coordinate becomes 3*(-5) = -15. Thus, the dilated point becomes A'(-15,-15).
For point B(-3,-2), the x-coordinate becomes 3*(-3) = -9, and the y-coordinate becomes 3*(-2) = -6. Thus, the dilated point becomes B'(-9,-6).
For point C(-7,-2), the x-coordinate becomes 3*(-7) = -21, and the y-coordinate becomes 3*(-2) = -6. Thus, the dilated point becomes C'(-21,-6).
For point D(-5,-1), the x-coordinate becomes 3*(-5) = -15, and the y-coordinate becomes 3*(-1) = -3. Thus, the dilated point becomes D'(-15,-3).
Therefore, after the dilation with a scale factor of 3 and a center point at the origin, the points become A'(-15,-15), B'(-9,-6), C'(-21,-6), and D'(-15,-3).
To describe the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0) on the given parallel lines, we need to consider the transformation of each point individually.
1. Point A:
- Original coordinates: A(-5, -5)
- Applying the dilation:
- x-coordinate: -5 * 3 = -15
- y-coordinate: -5 * 3 = -15
- Transformed coordinates: A'(-15, -15)
2. Point B:
- Original coordinates: B(-3, -2)
- Applying the dilation:
- x-coordinate: -3 * 3 = -9
- y-coordinate: -2 * 3 = -6
- Transformed coordinates: B'(-9, -6)
3. Point C:
- Original coordinates: C(-7, -2)
- Applying the dilation:
- x-coordinate: -7 * 3 = -21
- y-coordinate: -2 * 3 = -6
- Transformed coordinates: C'(-21, -6)
4. Point D:
- Original coordinates: D(-5, -1)
- Applying the dilation:
- x-coordinate: -5 * 3 = -15
- y-coordinate: -1 * 3 = -3
- Transformed coordinates: D'(-15, -3)
Therefore, the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0) on the given parallel lines is as follows:
- Point A is transformed to A'(-15, -15)
- Point B is transformed to B'(-9, -6)
- Point C is transformed to C'(-21, -6)
- Point D is transformed to D'(-15, -3)
To describe the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0), we need to apply the dilation to each point and observe the changes.
Let's start by finding the coordinates of the new points after the dilation.
Point A(-5,-5):
To dilate this point, we need to multiply both the x-coordinate and the y-coordinate by the scale factor of 3.
x-coordinate of A' = -5 * 3 = -15
y-coordinate of A' = -5 * 3 = -15
So, the new coordinates of A' after the dilation are (-15, -15).
Point B(-3,-2):
Using the same procedure, we can find the new coordinates of B' after the dilation.
x-coordinate of B' = -3 * 3 = -9
y-coordinate of B' = -2 * 3 = -6
Thus, the new coordinates of B' after the dilation are (-9, -6).
Now, we can compare the new coordinates A' (-15, -15) and B' (-9, -6) with the original coordinates of points C (-7,-2) and D (-5,-1) on line CD.
From the given information, we can see that the y-coordinates of both A' and B' are negative, while the y-coordinates of C and D are the same. This means that the dilation has vertically compressed the line.
Moreover, if we compare the x-coordinates, we observe that A' and B' are both more negative than C and D. This indicates that the line has been translated to the left.
In summary, the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0) is that line AB has been vertically compressed and translated to the left.