To find the new coordinates of the vertices after a rotation, we will apply the appropriate rotation transformation rules:

7. Rotation of Trapezoid QRST

• Rotation: 90° clockwise.
• Original vertices:
  • Q(2, 1)
  • R(2, 5)
  • S(4, 5)
  • T(8, 1)

Rotation Rule for 90° clockwise:
$(x, y) \rightarrow (y, -x)$

Applying the rule to each vertex:

1. Q(2, 1):
   New point $Q'$ = (1, -2)
2. R(2, 5):
   New point $R'$ = (5, -2)
3. S(4, 5):
   New point $S'$ = (5, -4)
4. T(8, 1):
   New point $T'$ = (1, -8)

8. Rotation of Triangle MNP

• Rotation: 270° clockwise.
• Original vertices:
  • M(-7, 6)
  • N(-1, 2)
  • P(-6, 0)

Rotation Rule for 270° clockwise (equivalent to 90° counterclockwise):
$(x, y) \rightarrow (-y, x)$

Applying the rule to each vertex:

1. M(-7, 6):
   New point $M'$ = (-6, -7)
2. N(-1, 2):
   New point $N'$ = (-2, -1)
3. P(-6, 0):
   New point $P'$ = (0, -6)

Final Coordinates:

• Trapezoid QRST (90° clockwise)

  • Q' = (1, -2)
  • R' = (5, -2)
  • S' = (5, -4)
  • T' = (1, -8)

• Triangle MNP (270° clockwise)

  • M' = (-6, -7)
  • N' = (-2, -1)
  • P' = (0, -6)

Would you like more details or have any questions?

Related Questions:

1. How do you find the coordinates after a 180° rotation?
2. What is the effect of a 270° counterclockwise rotation on a coordinate?
3. How do you reflect a shape over the x-axis or y-axis?
4. What are the rules for rotating a point 90° counterclockwise?
5. Can you explain how to translate a shape on the coordinate plane?

Tip:

When rotating shapes on the coordinate plane, remember that rotating clockwise or counterclockwise by 90°, 180°, or 270° has specific rules for swapping and negating coordinates.