Math Jeopardy: Coordinate Grids and Transformations

Coordinates

100

What is the coordinate of the point located 3 units right and 2 units up from the origin?

(3,2)

200

Define what an ordered pair is in the context of a coordinate grid.

An ordered pair in the context of a coordinate grid is a set of two numbers written in parentheses, like (x, y), that represents the location of a point on the grid.

300

What is the quadrant of the point (-4, 5)?

III

400

Explain how to convert the point (6, -3) to its reflection over the x-axis.

1. Identify the original point: The point is (6, -3).

   • The x-coordinate stays the same because reflections over the x-axis do not affect horizontal position.
   • The y-coordinate changes to its opposite (positive or negative) because the reflection flips the point vertically.

2. Flip the y-coordinate:

   • The original y-coordinate is -3.
   • The opposite of -3 is +3.

3. Write the new ordered pair: The reflected point is (6, 3).

✅ Final Answer: (6, 3)

500

If a point is located at (2, -1), what are the coordinates after moving it 4 units left and 3 units up?

(-2,2)

Plotting Points

100

On a coordinate grid, where would you plot the point (0, 0)?

At the origin

200

What are the coordinates of a point that is located 5 units left and 4 units down from the origin?

(-5,-4)

300

If you plot the points (2, 3) and (2, -3), what do you notice about their positions?

They reflect over the x-axis

400

Describe the steps to plot the point (-2, 4) on a coordinate grid.

Move two units to the left and four units up

500

 If the point (3, 2) is plotted on the grid, what would be its location if it is moved 2 units down and 1 unit right?

(1,3)

Translations

100

What does it mean to translate a point on a coordinate grid?

To slide a point to a new point on a coordinate grid.

200

If the point (1, 1) is translated 3 units right and 2 units down, what are its new coordinates?

(4, -1)

300

Describe how to translate the point (-3, 2) 4 units left.

1. Identify the original coordinates: (-3, 2)
2. Move left:
   • Moving left affects the x-coordinate (horizontal position).
   • Subtract 4 from the x-coordinate: −3−4=−7-3 - 4 = -7−3−4=−7
3. The y-coordinate stays the same because the movement is only left (no vertical change).

✅ Final Answer: The new coordinates are (-7, 2).

400

Explain what happens to the coordinates of a triangle when it is translated up by 5 units.

All points of the triangle will slide 5 units upward

500

A point at (4, 5) is translated to (8, 5). What can you say about the movement of this point?

The point moved 4 units to the right

Rotations

100

What is a rotation in relation to coordinate grids?

A spin around a designated coordinate point.

200

If a point (2, 3) is rotated 90 degrees counterclockwise around the origin, what are its new coordinates?

(-3, 2)

300

Describe the effect of rotating a point 180 degrees around the origin.

The point will appear exactly opposite from where it was on the coordinate grid.

400

How do you determine the new coordinates of a point after a 270-degree rotation?

• Take the original point (x, y).
• Swap the coordinates.
• Change the sign of the new x-coordinate (the original y-coordinate).

500

 If a triangle with vertices at (1, 1), (1, 3), and (3, 1) is rotated 90 degrees clockwise, what are the new coordinates of the vertices?

The new coordinates of the triangle are:
(1, -1), (3, -1), and (1, -3) ✅

Reflections

100

What is a reflection in coordinate geometry?

A mirror over an axis

200

How do you reflect the point (3, 4) over the y-axis?

• Identify the original point:
  The point is (3, 4), where:

  • The x-coordinate is 3.
  • The y-coordinate is 4.

• Apply the Reflection Rule:
  When reflecting over the y-axis, the x-coordinate changes to its opposite, while the y-coordinate stays the same.

  The rule is:
  (x, y) → (-x, y)

300

If a point is reflected over the x-axis, what happens to its y-coordinate?

You will change the sign of the y coordinate (ex. positive to negative).

400

What are the coordinates of the reflection of the point (-2, -5) over the line y = 0?

(-2, 5)

500

Describe the process to find the reflection of the point (5, 6) over the line x = 3.

To reflect the point, move the same distance to the other side of the line.
Since the point is 2 units to the right of the line, its reflection will be 2 units to the left of the line.

Find the new coordinates

The x-coordinate of the reflected point will be:
3 - 2 = 1.

The y-coordinate stays the same because the reflection is only horizontal.
The y-coordinate is 6.

Final Answer:

The reflection of the point (5, 6) over the line x = 3 is (1, 6).