Use the image to answer the question.

Question

A coordinate plane shows two pentagons crossing all four quadrants. The horizontal axis ranges from negative 2 to 5 in unit increments. The vertical axis ranges from negative 2 to 5 in unit increments. Five points labeled upper A upper B upper C upper D upper E form a solid line pentagon. The unmarked approximate coordinates are as follows: upper A is at left parenthesis 0 comma 5 right parenthesis, upper B is at left parenthesis negative 2 comma 4 right parenthesis, upper C is at left parenthesis negative 1 comma 2 right parenthesis, upper D is at left parenthesis 1.1 comma 3.1 right parenthesis, and upper E is at left parenthesis 1.4 comma 5.2 right parenthesis. Point upper F is marked at left parenthesis 3 comma 3 right parenthesis. Five points labeled upper G upper H upper I upper J upper K form a dotted line pentagon. The unmarked approximate coordinates are as follows: upper G is at left parenthesis 4 comma negative 1 right parenthesis, upper H is at left parenthesis 2.9 comma 1.1 right parenthesis, upper I is at left parenthesis 0.7 comma 1.5 right parenthesis, upper J is at left parenthesis 1 comma 0 right parenthesis, and upper K is at left parenthesis 2 comma negative 2 right parenthesis. No angles are marked.

Which angle corresponds to angle K
in the rotation of pentagon ABCDE
90°
counterclockwise around point F
? Enter the number for the correct angle.

1 = angle A

2 = angle B

3 = angle C

4 = angle D

5 = angle E


(1 point)

Skip to navigation

Answer 1

To determine which angle corresponds to angle K in the rotation of pentagon ABCDE 90° counterclockwise around point F, we first need to understand the positioning of the points of pentagon ABCDE as well as how the rotation affects the points.

Point F is located at (3, 3).

Now, let's examine the coordinates of pentagon ABCDE:

• A (0, 5)
• B (-2, 4)
• C (-1, 2)
• D (1.1, 3.1)
• E (1.4, 5.2)

Next, we focus on rotating these points 90° counterclockwise around point F. The transformation for a 90° counterclockwise rotation of point (x, y) around point (h, k) can be calculated as follows:

1. Translate the point to origin:
   • New x = (y - k) + h
   • New y = - (x - h) + k

Now we apply this transformation to each point:

Let's calculate this for:

• Point A (0, 5)

  • Translated: (0 - 3, 5 - 3) = (-3, 2)
  • After rotation: (2 + 3, -(-3) + 3) = (5, 6) --> Corresponds to a point not given.

• Point B (-2, 4)

  • Translated: (-2 - 3, 4 - 3) = (-5, 1)
  • After rotation: (1 + 3, 5 + 3) = (4, 8) --> Corresponds to a point not given.

• Point C (-1, 2)

  • Translated: (-1 - 3, 2 - 3) = (-4, -1)
  • After rotation: (-1 + 3, 4 + 3) = (2, 7) --> Corresponds to a point not given.

• Point D (1.1, 3.1)

  • Translated: (1.1 - 3, 3.1 - 3) = (-1.9, 0.1)
  • After rotation: (0.1 + 3, -(-1.9) + 3) = (3.1, 4.9) --> Corresponds to a point not given.

• Point E (1.4, 5.2)

  • Translated: (1.4 - 3, 5.2 - 3) = (-1.6, 2.2)
  • After rotation: (2.2 + 3, -(-1.6) + 3) = (5.2, 4.6) --> Corresponds to a point not given.

To understand what angle K looks like, it’s drawn in reference to points - observing the position of pentagon GHIJK. By carefully comparing, angle K aligns with angle B at point (-2,4) based on the location.

Thus, the correct answer is:

2 = angle B