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Identify and Perform Rotations

Students rotate figures 90°, 180°, and 270° clockwise and counterclockwise about the origin or a given point. They apply coordinate rules for each rotation and confirm that angles and lengths are preserved.

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Identify and Perform Rotations

Grade 8 · Geometry: Transformations · question 1 of 3

0 of 20

20 rungs. A star at the top.

C−8−6−4−22468−8−6−4−224680

Once point C is rotated 90 degrees counterclockwise about the origin, report the y-coordinate of C′.

Perform the move.

How it is taught

0:00 of 4:10

A rotation spins a figure about a fixed point.

A ninety-degree turn about the origin swaps coordinates and changes one sign.

D−8−6−4−22468−8−6−4−224680

Read it: Rotations about the origin

Point S(4, 1) turns 90° counterclockwise about the origin. A quarter turn counterclockwise follows (x, y) → (−y, x), so S lands at S′(−1, 4).

  1. Read the turn: 90°, 180° or 270°, and which way.
  2. As rules: 90° counterclockwise is (x, y) → (−y, x), and 180° is (x, y) → (−x, −y).
  3. 90° clockwise is the same as 270° counterclockwise: (x, y) → (y, −x).

A point in the first quadrant turns counterclockwise into the second quadrant.

S is 4 across and 1 up; after a quarter turn it is 1 to the left and 4 up.

A turn keeps the point's distance from the origin.

A quarter turn counterclockwise sends (x, y) to (−y, x).

Turning the wrong way: sending S(4, 1) to (1, −4), which is a clockwise turn.

Counterclockwise goes from the first quadrant into the second, where x is negative: S′ is (−1, 4).

Point R(−7, 5) is rotated 90° counterclockwise about the origin. What is the x-coordinate of R′? — −5. A quarter turn counterclockwise sends (x, y) to (−y, x): the new x is the opposite of 5, −5.

Rotate A(4, 2) by 90° counterclockwise about the origin

Rotations spin a figure around a fixed point. Today we'll spin a point ninety degrees counterclockwise around the origin.

Here's our coordinate plane, and our starting point — A at four, two.

Grade 8 · 90° counterclockwise rotation about the origin

Where will A land after a quarter-turn counterclockwise?

For a ninety-degree counterclockwise rotation around the origin, the rule is: swap x and y, then flip the sign of the new x.

First, swap. The four moves to the y spot, and the two moves to the x spot.

Now flip the sign of that new x. Positive two becomes negative two.

So A prime lands at negative two, four.

Let's plot A prime on the plane.

Watch the quarter-turn — A swings up and to the left to its new home.

Both points sit the same distance from the origin. Rotations always preserve lengths and angles.

A at four, two rotates ninety degrees counterclockwise to A prime at negative two, four. Nice work!

Now you try. Read the x-coordinate of A prime. Type x for A-prime.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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