correct answers only

Question 1
A)
Use the image to answer the question.

Parallelogram upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 9 to 10 in increments of 1. The y-axis ranges from negative 9 to 10 in increments of 1.

Suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 12. What would be the coordinates of vertex D′?

(1 point)
($$,$$)
Question 2
A)
Use the image to answer the question.

Parallelogram upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 9 to 10 in increments of 1. The y-axis ranges from negative 9 to 10 in increments of 1.

What would be the coordinates of vertex B′ of the parallelogram if it were dilated with respect to the origin using a magnitude of 3?

(1 point)
($$,$$)
Question 3
A)
Use the image to answer the question.

Triangle upper A upper B upper C is graphed on a coordinate plane. The x-axis ranges from 0 to 30 in increments of 5. The y-axis ranges from 0 to 30 in increments of 5.

Jill is trying to dilate the triangle on a coordinate plane in reference to the origin using a magnitude of 15. What are the vertices of the dilated triangle A′B′C′? Enter the number of the correct option.

Option #1: A′(45,1), B′(4,5), C′(6,65)

Option #2: A′(4,54), B′(5,5), C′(6,6)

Option #3: A′(4,1), B′(4,5), C′(6,15)

(1 point)
Option #$$ shows the new vertices of the dilated triangle.
Question 4
A)
Use the image to answer the question.

A coordinate plane's axes range from negative 1 to 4 by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A, upper B, upper C, and upper D, respectively.

Suppose you dilate the rectangle on the coordinate plane using a magnitude of 12 and the center of dilation at (1,1). What would be the corresponding ordered pair to the current point D?

(1 point)
The new ordered pair for point D′ would be at ($$,$$).
Question 5
A)
Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 6 to 7 and its y-axis ranges from negative 5 to 5, both by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A, upper B, upper C, and upper D, respectively.

Rectangle ABCD is drawn on a coordinate plane. If the rectangle were dilated using a magnitude of 3 and center of dilation at (3,0), what would be the corresponding ordered pair to point A?

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

I'm unable to view the images referenced in your questions, so I cannot provide specific coordinate answers without that information. However, I can offer you guidance on how to calculate the dilated coordinates if you know the original coordinates of the points.

General Method for Dilation

  1. Dilation with respect to the origin: For a point \((x, y)\) and a dilation factor \(k\), the new coordinates after dilation are given by:

    • New coordinates: \((kx, ky)\)
  2. Dilation with respect to a point \((h, k)\): For a point \((x, y)\) and a dilation factor \(m\) with the center of dilation at \((h, k)\):

    • New coordinates: \((h + m(x - h), k + m(y - k))\)

Example Calculations

  • If point D is located at (x_D, y_D) and you're dilating with a factor of \(k\), the new coordinates would be \((k \cdot x_D, k \cdot y_D)\) for dilation at the origin.
  • For a center of dilation at (h, k), use the formula above.

If you provide the specific coordinates of points A, B, C, and D, I can help you calculate the resulting dilated coordinates directly!