a segment with a length 7 cm is dilated with center 0 and scale factor 1/4. The image of the segment is then dilated with center p and scale factor 2. find the length of the image after each dilation.
the center of dilation does not matter
just multiply the dilation factors
To find the length of the image after each dilation, we will first calculate the length of the image after the first dilation and then use that result to find the length of the final image after the second dilation.
Let's start by finding the length of the image after the first dilation with a scale factor of 1/4.
Given that the original segment has a length of 7 cm, we can multiply it by the scale factor to find the length of the image after the first dilation:
Length of the image after first dilation = Scale factor * Length of the original segment
= (1/4) * 7 cm
= 7/4 cm
= 1.75 cm
So, the length of the image after the first dilation is 1.75 cm.
Now, let's find the length of the final image after the second dilation with a scale factor of 2.
Since we are applying the second dilation with center p, we need to find the image of the 1.75 cm segment after this second dilation.
Using the same formula as before:
Length of the final image = Scale factor * Length of the previous image
= 2 * 1.75 cm
= 3.5 cm
Therefore, the length of the final image after both dilations is 3.5 cm.