#11 The coordinate of rectangle ABCD are given. Find the coordinates of its image after a dilation with the scale factor of 2. * A (2,4) B (-3, -1) C (0,9) D (6,-4)
#10 On a blueprint, 1 inch = 13 feet. If the dimensions of the playroom on the blueprint are 0.35 inches x 1.25 inches, what are its actual measurements?
11. ?????
10. 1/13 x 0.35/m
1 x m = 13 x 0.35
m = 4.55
1/13 x 1.25/m
1 x m = 13 x 1.25
m = 16.25
Your figures for 10 are correct. However, that is sure a strange playroom -- 4.55 feet wide and 16.25 feet long???
I know right! Math sure is strange......
To find the coordinates of the image of rectangle ABCD after a dilation with a scale factor of 2, we need to multiply each coordinate by the scale factor.
Let's go step by step:
1. The coordinates of rectangle ABCD are:
- A (2,4)
- B (-3, -1)
- C (0,9)
- D (6,-4)
2. To find the image coordinates, we will multiply each coordinate by the scale factor of 2.
For point A (2,4):
- Multiplying the x-coordinate, 2, by 2 gives us 4.
- Multiplying the y-coordinate, 4, by 2 gives us 8.
So the new coordinates for A are (4, 8).
For point B (-3, -1):
- Multiplying the x-coordinate, -3, by 2 gives us -6.
- Multiplying the y-coordinate, -1, by 2 gives us -2.
So the new coordinates for B are (-6, -2).
For point C (0,9):
- Multiplying the x-coordinate, 0, by 2 gives us 0.
- Multiplying the y-coordinate, 9, by 2 gives us 18.
So the new coordinates for C are (0, 18).
For point D (6,-4):
- Multiplying the x-coordinate, 6, by 2 gives us 12.
- Multiplying the y-coordinate, -4, by 2 gives us -8.
So the new coordinates for D are (12, -8).
Therefore, the coordinates of the image of rectangle ABCD after a dilation with a scale factor of 2 are:
A' (4, 8)
B' (-6, -2)
C' (0, 18)
D' (12, -8).
Let me know if there is anything else I can help you with!