Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Reflecting Points Across the Axes

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
Coordinate planeSpanish: Plano cartesiano	A grid with a line going across and a line going up to plot points.	A grid with a horizontal line (x-axis) crossing a vertical line (y-axis), making four sections
Ordered pairSpanish: Par ordenado	Two numbers (x, y) that tell where a point is on a grid.	(3, 5) means move right 3 from the origin, then up 5
OriginSpanish: Origen	The point (0, 0) where the two grid lines cross.	The starting point at the center where both axes cross — (0, 0)
QuadrantSpanish: Cuadrante	One of the four parts of a coordinate grid, numbered I to IV.	Quadrant IV is lower right
ReflectionSpanish: Reflexión	A flipped, mirror image across a line.	(4, 1) → (4, −1)
IntegerSpanish: Número entero	Whole numbers and their opposites, like -2, -1, 0, 1, 2.	..., -3, -2, -1, 0, 1, 2, 3, ...

How it worksWorked examplereflecting a point across each axis

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Point R sits at (3.25, −5.5). Find the reflection of R across the x-axis and across the y-axis.

A reflection across the x-axis keeps x the same and flips the sign of y.
Across the x-axis: (3.25, −5.5) → (3.25, 5.5)
A reflection across the y-axis keeps y the same and flips the sign of x.
Across the y-axis: (3.25, −5.5) → (−3.25, −5.5)

Answer: Across the x-axis R lands at (3.25, 5.5); across the y-axis it lands at (−3.25, −5.5).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Point S sits at (−2.75, 6.5). Find the reflection of S across the x-axis and across the y-axis.

Across the x-axis the -coordinate stays and the -coordinate flips.
Across the x-axis: (−2.75, 6.5) → ( , )
Across the y-axis the -coordinate stays and the -coordinate flips.
Across the y-axis: (−2.75, 6.5) → ( , )

Answer:the two reflection points

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

Reflecting across the -axis gives .
The -coordinate stays the same because .
The image lands in Quadrant because its signs are .
Both points sit units from the mirror line, so .

Word bank reflectionmirror linex-axisy-axisimageordered pairquadrantsignoppositedistanceflipstays the same

Watch outA common mistake

A common mistake in Graph on the Coordinate Plane is swapping the order of the coordinates — moving up/down first instead of right/left first. For example, when plotting (5, 2), students often move up 5 and right 2, landing on the wrong point (2, 5) instead of (5, 2). Remember: the x-coordinate (first number) always tells you how far to move right or left along the x-axis; the y-coordinate (second number) tells you how far up or down along the y-axis.

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Reflecting Points Across the Axes

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

1Complete each step, then write the final answer.

To plot (9, 1), how many units do you move up from the origin?
Show your work
Hint The second number is y. It tells how far to move up.
Final answer:
2Complete each step, then write the final answer.

A point is 4 units right and 6 units up from the origin. What is its y-coordinate?
Show your work
Hint y tells how far up the point is.
Final answer:
3Complete each step, then write the final answer.

To plot (5, 3), how many units do you move right from the origin?
Show your work
Hint The first number is x. It tells how far to move right.
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Reflecting Points Across the Axes

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

1Complete each step, then write the final answer.

Tia plots (3, 8). She moves 8 units right and 3 units up. Is she right? How many units right should she move?
Show your work
Final answer:
2Complete each step, then write the final answer.

To plot (−4, −1.5), how many units down do you move from the origin?
Show your work
Final answer:
3Complete each step, then write the final answer.

To plot (8, 4), how many units do you move up from the origin?
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Reflecting Points Across the Axes

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

1Circle the letter of the best answer. Show how you know.
Starting at the origin, which point is located by moving 4 units LEFT and 3 units UP?
1. A(3, −4)
2. B(−3, 4)
3. C(−4, 3)
4. D(4, 3)
Show your work
2Complete each step, then write the final answer.

Ken says (−6, 1) and (1, −6) are the same point because they use the same numbers. To plot (1, −6), how many units down do you move?
Show your work
Final answer:
3Complete each step, then write the final answer.

To plot (−0.5, −4.5), how many units left do you move from the origin?
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help