Question
Suppose this triangle in the coordinate plane is dilated, with a center of dilation at the origin, using a scale factor of 12 . What would be the coordinates of the new vertices X′Y′Z′ (1 point) Responses X′(0,2), Y′(4,−2) and Z′(5,0) X′(0,2), Y′(4,−2) and Z′(5,0) X′(4,8), Y′(12,0) and Z′(14,4) X′(4,8), Y′(12,0) and Z′(14,4) X′(23.43), Y′(2,0) and Z′(73,23) X′(23.43), Y′(2,0) and Z′(73,23) X′(1,2), Y′(3,0) and Z′(72,1). X 2,4 Z 7,2 Y 6,0. CHOOSE ONE EVEN IF WRONG
Answers
GPT-4o mini
To find the coordinates of the new vertices after the triangle has been dilated with a center of dilation at the origin and a scale factor of 12, we start with the original vertices of the triangle.
The original vertices are:
- \(X(2, 4)\)
- \(Y(6, 0)\)
- \(Z(7, 2)\)
To apply the dilation from the origin with a scale factor of 12, we multiply both the x-coordinate and the y-coordinate of each vertex by the scale factor (12):
1. For \(X(2, 4)\):
\[
X' = (2 \times 12, 4 \times 12) = (24, 48)
\]
2. For \(Y(6, 0)\):
\[
Y' = (6 \times 12, 0 \times 12) = (72, 0)
\]
3. For \(Z(7, 2)\):
\[
Z' = (7 \times 12, 2 \times 12) = (84, 24)
\]
So the new vertices are:
- \(X'(24, 48)\)
- \(Y'(72, 0)\)
- \(Z'(84, 24)\)
Since none of the provided options exactly match our results and we are asked to choose one even if wrong, considering the proximity:
- None of the options \(X'(0,2), Y'(4,-2), Z'(5,0)\), \(X'(4,8), Y'(12,0), Z'(14,4)\), \(X'(23.43), Y'(2,0), Z'(73,23)\), and \(X'(1,2), Y'(3,0), Z'(72,1)\) closely resemble the results we obtained.
Thus, if one must be chosen, you’d probably stick with the second option \(X'(4,8),Y'(12,0),Z'(14,4)\) as it contains integer values which could relate to a scaling that might have been incorrectly inferred. But remember that they are not the correct identified dilation coordinates for this problem.
The original vertices are:
- \(X(2, 4)\)
- \(Y(6, 0)\)
- \(Z(7, 2)\)
To apply the dilation from the origin with a scale factor of 12, we multiply both the x-coordinate and the y-coordinate of each vertex by the scale factor (12):
1. For \(X(2, 4)\):
\[
X' = (2 \times 12, 4 \times 12) = (24, 48)
\]
2. For \(Y(6, 0)\):
\[
Y' = (6 \times 12, 0 \times 12) = (72, 0)
\]
3. For \(Z(7, 2)\):
\[
Z' = (7 \times 12, 2 \times 12) = (84, 24)
\]
So the new vertices are:
- \(X'(24, 48)\)
- \(Y'(72, 0)\)
- \(Z'(84, 24)\)
Since none of the provided options exactly match our results and we are asked to choose one even if wrong, considering the proximity:
- None of the options \(X'(0,2), Y'(4,-2), Z'(5,0)\), \(X'(4,8), Y'(12,0), Z'(14,4)\), \(X'(23.43), Y'(2,0), Z'(73,23)\), and \(X'(1,2), Y'(3,0), Z'(72,1)\) closely resemble the results we obtained.
Thus, if one must be chosen, you’d probably stick with the second option \(X'(4,8),Y'(12,0),Z'(14,4)\) as it contains integer values which could relate to a scaling that might have been incorrectly inferred. But remember that they are not the correct identified dilation coordinates for this problem.