Use the image to answer the question.

Question

Polygon upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 10 to 10 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

Paul is trying to dilate the figure in the image using a magnitude of 2 with reference to the origin. At what points would he draw the new vertices A′B′C′
?

(1 point)
Responses

A′(−6,6)
, B′(2,10)
, C′(8,−2)
and D′(2,−10)
upper A prime left parenthesis negative 6 comma 6 right parenthesis , upper B prime left parenthesis 2 comma 10 right parenthesis , upper C prime left parenthesis 8 comma negative 2 right parenthesis and upper D prime left parenthesis 2 comma negative 10 right parenthesis

A′(−1,5)
, B′(3,7)
, C′(6,1)
, and D′(3,−3)
upper A prime left parenthesis negative 1 comma 5 right parenthesis , upper B prime left parenthesis 3 comma 7 right parenthesis , upper C prime left parenthesis 6 comma 1 right parenthesis , and upper D prime left parenthesis 3 comma negative 3 right parenthesis

A′(−5,1)
, B′(−1,3)
, C′(2,−3)
and D′(−1,−7)
upper A prime left parenthesis negative 5 comma 1 right parenthesis , upper B prime left parenthesis negative 1 comma 3 right parenthesis , upper C prime left parenthesis 2 comma negative 3 right parenthesis and upper D prime left parenthesis negative 1 comma negative 7 right parenthesis

A′(−32,32)
, B′(12,52)
, C′(2,−12)
and D′(12,−52)

Answer 1

To find the coordinates of the vertices after dilating the original polygon ABCD by a magnitude of 2 with respect to the origin, you multiply each of the x and y coordinates of the original vertices by 2.

Let's represent the original vertices as:

• A(x₁, y₁)
• B(x₂, y₂)
• C(x₃, y₃)
• D(x₄, y₄)

After the dilation, the new vertices A′, B′, C′, and D′ will be:

• A′(2 * x₁, 2 * y₁)
• B′(2 * x₂, 2 * y₂)
• C′(2 * x₃, 2 * y₃)
• D′(2 * x₄, 2 * y₄)

However, since we don't have the original coordinates from the image provided, we cannot compute the new coordinates directly.

You will need to check the original coordinates of each vertex from the image, apply the dilation formula by multiplying each coordinate by 2, and then match the results to identify the correct option among those provided.

If you can share the original coordinates of the vertices, I can help you with the calculations!