Question
A triangle is drawn on a coordinate plane. Dilate the figure with a magnitude of 3 in reference to the origin. What are the coordinates of the new vertices of A′B′C′ ? (1 point) Responses A′(−6,−15) , B′(0,9) , and C′(18,−9) upper A prime left parenthesis negative 6 comma negative 15 right parenthesis , upper B prime left parenthesis 0 comma 9 right parenthesis , and upper C prime left parenthesis 18 comma negative 9 right parenthesis A′(−5,−8) , B′(−3,0) , and C′(3,0) upper A prime left parenthesis negative 5 comma negative 8 right parenthesis , upper B prime left parenthesis negative 3 comma 0 right parenthesis , and upper C prime left parenthesis 3 comma 0 right parenthesis A′(1,−2) , B′(3,6) , and C′(9,0) upper A prime left parenthesis 1 comma negative 2 right parenthesis , upper B prime left parenthesis 3 comma 6 right parenthesis , and upper C prime left parenthesis 9 comma 0 right parenthesis A′(−23,−53) , B′(0,1) , and C′(2,−1) upper A prime left parenthesis negative Start Fraction 2 over 3 End Fraction comma negative Start Fraction 5 over 3 End Fraction right parenthesis , upper B prime left parenthesis 0 comma 1 right parenthesis , and upper C prime left parenthesis 2 comma negative 1 right parenthesis
A -2, -5
B 0, 3
C 6, -3
A -2, -5
B 0, 3
C 6, -3
Answers
GPT-4o mini
To dilate a figure with a magnitude of 3 in reference to the origin, you multiply each coordinate of the vertices by the dilation factor.
If the original coordinates of the triangle are:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
After dilation, the new coordinates will be:
- A' = (3 * x₁, 3 * y₁)
- B' = (3 * x₂, 3 * y₂)
- C' = (3 * x₃, 3 * y₃)
You have provided several possible sets of new vertex coordinates, but to determine the correct ones, we need to apply the dilation to the original coordinates.
If you can provide the original coordinates of the vertices A, B, and C, I can calculate the new coordinates A', B', and C' for you.
If the original coordinates of the triangle are:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
After dilation, the new coordinates will be:
- A' = (3 * x₁, 3 * y₁)
- B' = (3 * x₂, 3 * y₂)
- C' = (3 * x₃, 3 * y₃)
You have provided several possible sets of new vertex coordinates, but to determine the correct ones, we need to apply the dilation to the original coordinates.
If you can provide the original coordinates of the vertices A, B, and C, I can calculate the new coordinates A', B', and C' for you.