Cartesian Plane and Transformations

Practice questions about the Cartesian plane, ordered pairs, and rules for translations, reflections, and rotations based on Grade 10 Week 3 notes.

What are the two axes that make up the Cartesian Plane?

The $x$-axis (horizontal axis) and the $y$-axis (vertical axis)

Where is the origin located in the Cartesian Plane?

$$(0,0)$$

What are the coordinates for points in Quadrant $I$ ($QI$)?

$$(+,+)$$

What are the coordinates for points in Quadrant $II$ ($QII$)?

$$(-,+)$$

What are the coordinates for points in Quadrant $III$ ($QIII$)?

$$(-,-)$$

What are the coordinates for points in Quadrant $IV$ ($QIV$)?

$$(+,-)$$

What does the $x$-coordinate of an ordered pair $(x, y)$ indicate?

left or right

What does the $y$-coordinate of an ordered pair $(x, y)$ indicate?

up or down

What parts of a geometric figure do coordinates describe?

The position of its vertices

What is the definition of a transformation?

A change in the position or orientation of a figure in the Cartesian plane

In any transformation, what is the original figure called?

preimage

In any transformation, what is the transformed figure called?

image

What type of transformation slides a figure to a new position?

Translation

What is the algebraic rule for a translation?

$$(x, y) \rightarrow (x+a, y+b)$$

What is the definition of a reflection?

flips a figure over a line of reflection

According to the transcript, what is the coordinate rule for a reflection over the $x$-axis?

$$(x, y)$$

What is the coordinate rule for a reflection over the $y$-axis?

$$(-x, y)$$

What is the coordinate rule for a reflection over the line $y=x$?

$$(y, x)$$

What is the coordinate rule for a reflection over the line $y=-x$?

$$(-y, -x)$$

What type of transformation turns a figure around a fixed point?

Rotation

What is the coordinate rule for a $90^\text{o}$ counter-clockwise ($CCW$) rotation about the origin?

$$(-y, x)$$

What is the coordinate rule for a $180^\text{o}$ rotation about the origin?

$$(-x, -y)$$

What is the coordinate rule for a $90^\text{o}$ clockwise ($CW$) rotation about the origin?

$$(y, -x)$$

During the transformations discussed in this lesson, what remains the same about the figure?

The figure keeps its shape and size