The center of dilation is (0,0) and the scale factor is 7. If A(3,4), then which is the distance between A and A'.
A. 5
B. 7
C. 30 <<<<
D. 35
It's right :^)
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1.A,D
2.B
3.B
4.B
5.A
6.D
7.C
8.A
9.D
10.C,F
Number one answers are a and c not a and d
30
To find the distance between point A and its image A' after dilation, we can use the formula for distance between two points in a coordinate plane.
The formula for distance between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Here, A(3, 4) is the original point, and the center of dilation is (0, 0) with a scale factor of 7. To find the image A', we need to perform dilation using the scale factor.
To dilate a point (x, y) about the origin (0, 0) with a scale factor of k, we multiply both x and y coordinates by the scale factor.
For point A(3, 4), after dilation with a scale factor of 7, the coordinates of A' will be:
A'(7 * 3, 7 * 4) = A'(21, 28)
Now, we can calculate the distance between A and A' using the formula mentioned earlier:
d = √((21 - 3)^2 + (28 - 4)^2)
= √(18^2 + 24^2)
= √(324 + 576)
= √900
= 30
Therefore, the correct distance between A and A' is 30, option C.
1. The dilation is an enlargement, the dilation has a scale factor of 3
2. (3/4,-9/4)
3. x=-10 and y=2.5
4. 1.2 cm
5. -1/8
6. 30 units
7. 12 cm
8. X'(-7.5,3.5) and Y'(-2.5,-5.5)
9. For a dilation, corresponding angles of the image and preimage are congruent. A dilation with a scale factor is an enlargement.