Plotting and Reflecting Points on the Coordinate Plane

Q: What is the origin on a coordinate plane?

The origin is the point (0, 0) where the x-axis and the y-axis cross. It is the starting point for every coordinate. You count left or right for the x-value and up or down for the y-value, always beginning from the origin.

Q: Which coordinate comes first, x or y?

The x-coordinate always comes first, then the y-coordinate, written as (x, y). You read across the horizontal x-axis first, then up or down the vertical y-axis. Keeping this order matters, because swapping the two numbers points to a different place on the coordinate plane.

Q: How do you reflect a point over the y-axis?

To reflect a point over the y-axis, change the sign of its x-coordinate and keep the y-coordinate the same. For example, the point (-3, 2) becomes (3, 2). The point moves to the opposite side of the y-axis but stays at the same height.

Q: How do you reflect a point over the x-axis?

To reflect a point over the x-axis, change the sign of its y-coordinate and keep the x-coordinate the same. For example, (-3, 2) becomes (-3, -2). The point moves to the opposite side of the x-axis but stays the same distance left or right.

Q: How do you reflect a point through the origin?

To reflect a point through the origin, change the sign of both the x-coordinate and the y-coordinate. For example, the point (-3, 2) becomes (3, -2). Both signs swap at the same time, so the point moves across to the opposite side of the origin.

Q: How do you reflect a shape on a coordinate plane?

To reflect a shape, reflect each of its vertices using the matching rule, then join the new points. For example, to reflect a triangle over the y-axis, change the sign of every vertex's x-coordinate, then connect the reflected points to draw the mirrored shape.

The coordinate plane locates every point with a pair (x, y): x tells you how far left or right, y how far up or down, so (3, 2) is 3 right and 2 up from the origin. Reflecting a point over the x-axis or y-axis changes the sign of one coordinate, while reflecting it in the origin changes the sign of both.

Plotting and Reflecting Points on the Coordinate Plane - introduction visual

Video Lesson

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$Plotting and Reflecting Points on the Coordinate Plane poster$

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Flashcards

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Coordinate system graph showing positive and negative numbers, with the origin marked at (0,0).

Locating points on a coordinate system with positive and negative coordinates.

Explanation on how to reflect (-3, 2) on a coordinate grid across the y-axis to (3, 2), by changing the sign of x.

Explanation on how to reflect (-3, 2) on a coordinate grid across the x-axis to (-3, -2), by changing the sign of y.

Explanation on how to reflect (-3, 2) on a coordinate grid across the origin to (3, -2), by changing both the signs of x and y.

Reflecting a triangle over the y-axis by changing the sign of the x-coordinate of all points.

The Coordinate System

The x-axis is horizontal and the y-axis is vertical.
The point where they meet is called the origin (0,0).

Practice Questions

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Q1Easy

What are the coordinates of a point located at 4 units to the left of the origin and 2 units below the origin?

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Interactive Activity

Visualise how points change when reflected across axes

Original Point

X-Coordinate4

Y-Coordinate3

Reflection Mode

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Students Also Ask

The questions students bump into most on this topic

What is the origin on a coordinate plane?

The origin is the point (0, 0) where the x-axis and the y-axis cross. It is the starting point for every coordinate. You count left or right for the x-value and up or down for the y-value, always beginning from the origin.

Which coordinate comes first, x or y?

The x-coordinate always comes first, then the y-coordinate, written as (x, y). You read across the horizontal x-axis first, then up or down the vertical y-axis. Keeping this order matters, because swapping the two numbers points to a different place on the coordinate plane.

How do you reflect a point over the y-axis?

To reflect a point over the y-axis, change the sign of its x-coordinate and keep the y-coordinate the same. For example, the point (-3, 2) becomes (3, 2). The point moves to the opposite side of the y-axis but stays at the same height.

How do you reflect a point over the x-axis?

To reflect a point over the x-axis, change the sign of its y-coordinate and keep the x-coordinate the same. For example, (-3, 2) becomes (-3, -2). The point moves to the opposite side of the x-axis but stays the same distance left or right.

How do you reflect a point through the origin?

To reflect a point through the origin, change the sign of both the x-coordinate and the y-coordinate. For example, the point (-3, 2) becomes (3, -2). Both signs swap at the same time, so the point moves across to the opposite side of the origin.

How do you reflect a shape on a coordinate plane?

To reflect a shape, reflect each of its vertices using the matching rule, then join the new points. For example, to reflect a triangle over the y-axis, change the sign of every vertex's x-coordinate, then connect the reflected points to draw the mirrored shape.

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