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)
Answers
GPT-4o mini
To dilate a triangle with a magnitude of 3 with respect to the origin, you need to multiply each coordinate of the original vertices by 3.
Let’s denote the original vertices of the triangle as A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). After dilation, the new coordinates become:
- A′(3 * x₁, 3 * y₁)
- B′(3 * x₂, 3 * y₂)
- C′(3 * x₃, 3 * y₃)
Since no original coordinates are provided, I cannot calculate the precise new coordinates. However, based on the information provided, please find the options you have, and you can check which one is the result of multiplying the original vertices' coordinates by 3.
For example, if the original coordinates were A(−2, −5), B(0, 3), C(6, −3), the new coordinates would be:
- A′(−2 * 3, −5 * 3) = (−6, −15)
- B′(0 * 3, 3 * 3) = (0, 9)
- C′(6 * 3, −3 * 3) = (18, −9)
Using this method, you can determine the resulting coordinates and check against the provided options. In this case, A'(-6, -15), B'(0, 9), and C'(18, -9) would be the correct dilation result if those were the original vertex coordinates.
Let’s denote the original vertices of the triangle as A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). After dilation, the new coordinates become:
- A′(3 * x₁, 3 * y₁)
- B′(3 * x₂, 3 * y₂)
- C′(3 * x₃, 3 * y₃)
Since no original coordinates are provided, I cannot calculate the precise new coordinates. However, based on the information provided, please find the options you have, and you can check which one is the result of multiplying the original vertices' coordinates by 3.
For example, if the original coordinates were A(−2, −5), B(0, 3), C(6, −3), the new coordinates would be:
- A′(−2 * 3, −5 * 3) = (−6, −15)
- B′(0 * 3, 3 * 3) = (0, 9)
- C′(6 * 3, −3 * 3) = (18, −9)
Using this method, you can determine the resulting coordinates and check against the provided options. In this case, A'(-6, -15), B'(0, 9), and C'(18, -9) would be the correct dilation result if those were the original vertex coordinates.