Graphing on the Coordinate Plane

Quiz: Monday, September 18, 2023

Graphic Organizer

Cartesian Coordinate System Graphic Organizer.pdf

Lesson 1: Coordinate Plane (Tuesday, September 12, 2023)

Coordinate Plane

The coordinate plane is a two-dimensional graph with a horizontal x-axis and a vertical y-axis.

Ordered Pair

Each position on the grid is known as an ordered pair or coordinates.

Origin

The point where the axes intersect is called the origin, identified by the ordered pair (0,0), with the x-axis value listed first, followed by the y-axis value.

Quadrants

The coordinate grid is divided into four sections known as quadrants, labeled as I, II, III, and IV.

Plotting Points on the Coordinate Plane

- An ordered pair is always in the form (x,y).

Move left or right on the x-axis.
Move up or down on the y-axis.
Plot the point where these locations intersect and label it using an ordered pair (x,y).

Practice Worksheet: Plot the points on the coordinate plane.

Graphing Coordinates.pdf

Lesson 2: Reflections of Points (Wednesday, September 13, 2023)

Reflection over the y-axis

The diagram below shows a reflection over the y-axis, where the x-coordinate changes sign.

For example, (2,4) becomes (-2,4) or vice versa.

It's important to note that the point and its reflection are always two units away from the y-axis horizontally.

In mathematical terms, (x,y) becomes (-x,y).

Reflection over the x-axis

On the other hand, reflection over the x-axis involves changing the sign of the y-coordinate.

For instance, (3,2) becomes (3,-2) or vice versa.

Again, the point and its reflection are vertically two units away from the x-axis.

In mathematical terms, (x,y) becomes (x,-y).

Practice Worksheet: Graph the new position of each point after the given reflection.

Reflection Point.pdf

Lesson 3: Distance Between Two Points (Thursday, September 14, 2023)

Horizontal Distance

The graph below shows six distance units from point A to point B.

To determine the horizontal distance, we examine the change in the x-coordinates from x = -4 to x = 2. We can count the distance from -4 to 2 on a number line, which gives us six units, just like how we relied on the grid.

Alternatively, we can use absolute value to express the distance between two values as | a - b | or | b - a |.

For instance, to find the distance from point A to point B, we examine the x-coordinates and get

| -4 - 2 | = 6 or | 2 - (-4) | = 6.

Vertical Distance

We can also apply this method to find the distance from point C to point D.

Since this distance is vertical, we must examine the y-coordinates from y = 1 to y = -3.

By counting, we can see that this distance is four units.

We can also use absolute value to express this distance as | 1 - (-3) | = 4 or | -3 - 1 | = 4.

Practice Worksheet: Find the distance between the original point and the reflection point.

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