What is the scale factor of the dilation where the points have gone from (-0.5,2), (-0.5,-1), (1.5,2), and (1.5,-1) to (-5,9), (3,9), (-5,-4), and (3,-4)?
To find the scale factor of a dilation, we can compare the length of any side of the pre-image to the corresponding side of the image.
Let's compare the length of the segment connecting (-0.5, 2) and (-0.5, -1) in the pre-image to the length of the segment connecting (-5, 9) and (-5, -4) in the image.
The length of the side in the pre-image is the difference in y-coordinates: 2 - (-1) = 3.
The length of the corresponding side in the image is the difference in y-coordinates: 9 - (-4) = 13.
Therefore, the scale factor is given by the ratio of the lengths:
scale factor = (length of side in image)/(length of side in pre-image) = 13/3.
Hence, the scale factor of the dilation is 13/3.
To find the scale factor of a dilation, we need to compare the corresponding distances between the coordinates before and after the dilation.
Let's start by calculating the horizontal and vertical distances between the original points:
Horizontal distance = 1.5 - (-0.5) = 2 units
Vertical distance = (-1) - 2 = -3 units
Now, let's calculate the horizontal and vertical distances between the transformed points:
Horizontal distance = 3 - (-5) = 8 units
Vertical distance = (-4) - 9 = -13 units
To find the scale factor, we need to compare the distances before and after the dilation:
Horizontal scale factor = (Horizontal distance after dilation) / (Horizontal distance before dilation)
= 8 / 2
= 4
Vertical scale factor = (Vertical distance after dilation) / (Vertical distance before dilation)
= -13 / -3
= 4.333 (rounded to three decimal places)
Therefore, the scale factor of the dilation is approximately 4 for both horizontal and vertical directions.
To find the scale factor of a dilation, we need to compare the distance between corresponding points before and after the dilation.
Let's take two corresponding points from the original shape and the image shape.
Original Shape: (-0.5, 2) and (1.5, 2)
Image Shape: (-5, 9) and (3, 9)
Distance in the original shape = √ [ (x2 - x1)^2 + (y2 - y1)^2 ]
= √ [ (1.5 - (-0.5))^2 + (2 - 2)^2 ]
= √ [ (2)^2 + (0)^2 ]
= √ [ 4 + 0 ]
= √4
= 2
Distance in the image shape = √ [ (x2 - x1)^2 + (y2 - y1)^2 ]
= √ [ (3 - (-5))^2 + (9 - 9)^2 ]
= √ [ (8)^2 + (0)^2 ]
= √ [ 64 + 0 ]
= √64
= 8
Therefore, the scale factor of the dilation is the ratio of the distance in the image shape to the distance in the original shape:
Scale Factor = Distance in the image shape / Distance in the original shape
= 8 / 2
= 4
So, the scale factor of the dilation is 4.