math 🥴

• What is the definition of probability?

  Probability is a measure of the likelihood that an event will occur.
• How do meteorologists use probability?


  They use it to predict the likelihood of various weather events.
• What are some real-world applications of probability?


  • Weather forecasting
  • Risk assessment in finance
  • Quality control in manufacturing
  • Decision-making in healthcare
• How do bar charts visually represent data?


  Bar charts use rectangular bars where the length or height is proportional to the value it represents.
• If a point at (-1, 4) is rotated 90° clockwise around the origin (0,0), what are its new coordinates?


  The new coordinates are (4, 1).
• What happens to the y-coordinate during a 90° clockwise rotation around the origin?


  The new y-coordinate becomes the negative of the original x-coordinate.
• How does the point (-1, 4) change after a 90° clockwise rotation around the origin?


  It becomes (4, 1).
• What is the correct transformation of the point (-1, 4) when rotated 90° clockwise around the origin?


  The transformation results in the coordinates (4, 1).
• What are the steps to rotate a point (x, y) 90° clockwise around the origin?


  • New x-coordinate = original y-coordinate
  • New y-coordinate = negative of original x-coordinate
• What happens to the x-coordinate during a 90° clockwise rotation around the origin?


  The new x-coordinate becomes the original y-coordinate.
• What are the new coordinates of the point (3, 2) after rotating it 90° clockwise around the origin (0,0)?


  The new coordinates are (2, -3).
• What remains unchanged during a rotation?


  The shape and size of the figure remain unchanged.
• What are the key components of rotation?


  1. The center of rotation
  2. The angle of rotation
  3. The direction (clockwise or counterclockwise)
• What is rotation in geometry?


  Rotation is a transformation that turns a figure around a fixed point called the center of rotation.
• If a point at (-4, 5) is reflected over the y-axis, what are its new coordinates?


  The new coordinates are (4, 5).
• What are the new coordinates of a triangle with vertices at (2, 3), (-1, 4), and (3, -2) after reflecting it over the y-axis?


  The new coordinates are (-2, 3), (1, 4), and (-3, -2).
• What are the new coordinates of the point (3, 2) after reflecting it over the y-axis?


  The new coordinates are (-3, 2).
• How do you reflect a figure over a line?

  1. Identify the line of reflection (e.g., x-axis, y-axis, a diagonal line).
  2. For each point, find the point on the opposite side of the line that is the same distance away.
• What is reflection in geometry?


  Reflection is a transformation that flips a figure over a line called the line of reflection.
• What are the new coordinates of a triangle with vertices at (0,0), (2,0), and (1,2) after translating it 3 units right and 1 unit down?


  The new coordinates are (3,-1), (5,-1), and (4,1).
• If a square is translated 3 units to the right and 2 units up, what happens to its position?

  The square moves to a new position without any other changes.
• What are the steps to translate a figure?


  1. Identify the direction (left, right, up, down) and distance to move.
  2. Shift all points of the figure the same distance in the specified direction.
• What does translation do to a geometric figure?


  Translation moves a figure a certain distance in a particular direction without changing its size, shape, or orientation.
• What are the key types of transformations in geometry?

  • Translation (sliding)
  • Reflection (flipping)
  • Rotation (turning)
  • Scaling (enlarging or reducing)
• What is the resulting figure after a transformation called?


  The resulting figure is called the image.
• What is the original figure called in a transformation?


  The original figure is called the pre-image.
• What are transformations in mathematics?


  Transformations are operations that change the position, size, or shape of a geometric figure.
• What are the new coordinates of the point (2, 1) after a 90° clockwise rotation around the origin?


  (1, -2)
• What are the new coordinates of the point (-3, 2) after a 90° clockwise rotation around the origin?


  (2, 3)
• What are the new coordinates of the point (0, -4) after a 90° clockwise rotation around the origin?


  (-4, 0)
• What are the new vertices of a triangle with vertices at (2, 1), (-3, 2), and (0, -4) after a 90° clockwise rotation around the origin?


  • (2, 1) becomes (1, -2)
  • (-3, 2) becomes (2, 3)
  • (0, -4) becomes (-4, 0)
• What are the new coordinates of the point (5, -3) after a 90° clockwise rotation around the origin?


  (-3, -5)
• What are the new vertices of a rectangle with vertices at (2, 4), (2, -1), (-3, -1), and (-3, 4) after a 90° clockwise rotation around the origin?


  • (2, 4) becomes (4, -2)
  • (2, -1) becomes (-1, -2)
  • (-3, -1) becomes (-1, 3)
  • (-3, 4) becomes (4, 3)
• What are the new coordinates of the point (0, 3) after a 90° clockwise rotation around the origin?


  (3, 0)
• What are the new coordinates of the point (-2, -1) after a 90° clockwise rotation around the origin?


  (-1, 2)
• What are the new coordinates of the point (4, -1) after a 90° clockwise rotation around the origin?


  (-1, -4)
• What are the new vertices of a triangle with vertices at (0, 3), (-2, -1), and (4, -1) after a 90° clockwise rotation around the origin?


  • (0, 3) becomes (3, 0)
  • (-2, -1) becomes (-1, 2)
  • (4, -1) becomes (-1, -4)
• What are the new vertices of a square with vertices at (1, 1), (1, -1), (-1, -1), and (-1, 1) after a 90° clockwise rotation around the origin?


  (1, -1), (-1, -1), (-1, 1), (1, 1)
• What are the coordinates of the point (-1, 1) after a 90° clockwise rotation?


  (1, 1)
• What are the final coordinates after rotating the points (1, -1), (-1, -1), and (-1, 1) 90° clockwise?


  (1, -1), (-1, -1), (-1, 1), (1, 1)