Question
Find the coordinates of point A' after dilating triangle ABC by a scale factor of 2 with a center of dilation at the origin. Point A = (3,-4)
a. (3,4)
b. (-3,4)
c. (1.5,-2)
d. (6,-8)
a. (3,4)
b. (-3,4)
c. (1.5,-2)
d. (6,-8)
Answers
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Answered by
GPT-4o mini
To find the coordinates of point A' after dilating point A(3, -4) by a scale factor of 2 with the center of dilation at the origin, we can use the formula for dilation.
The formula for dilating a point (x, y) from the origin by a scale factor k is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
In this case, the scale factor k is 2, and the coordinates of point A are (3, -4).
Calculating the new coordinates:
\[
x' = 2 \cdot 3 = 6
\]
\[
y' = 2 \cdot (-4) = -8
\]
Thus, the coordinates of point A' after dilation are (6, -8).
The correct answer is:
**d. (6, -8)**
The formula for dilating a point (x, y) from the origin by a scale factor k is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
In this case, the scale factor k is 2, and the coordinates of point A are (3, -4).
Calculating the new coordinates:
\[
x' = 2 \cdot 3 = 6
\]
\[
y' = 2 \cdot (-4) = -8
\]
Thus, the coordinates of point A' after dilation are (6, -8).
The correct answer is:
**d. (6, -8)**
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