50+ Rotations worksheets for 7th Class on Quizizz | Free & Printable - Free Printable

Here are the step-by-step solutions for the problems shown in your worksheet.

Problem 1

Question: How many degrees was the figure rotated?

1. Identify a reference point: Look at point $O$ on the original figure (the black one). It is located at the origin $(0,0)$. Now look at point $O'$ on the rotated figure (the blue one). It is also at $(0,0)$. This tells us the rotation is around the origin.
2. Pick another easy point: Let's look at point $E$ on the bottom of the original figure. Looking at the grid, point $E$ is at coordinates $(2, 0)$ because it is 2 units to the right of the y-axis and on the x-axis.
3. Find the matching point: Find point $E'$ on the blue figure. Point $E'$ is at coordinates $(0, 2)$ because it is 2 units up on the y-axis.
4. Determine the movement: To get from $(2, 0)$ [Right] to $(0, 2)$ [Up], the figure moved a quarter turn to the left.
5. Conclusion: A quarter turn to the left is called a 90-degree counterclockwise rotation.

Correct Option: C

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Problem 2

Question: If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

1. Find the starting coordinate: Locate point $A$ on the graph. It is 3 units to the right and 5 units up. So, the coordinate of $A$ is $(3, 5)$.
2. Apply the rule: The rule for rotating a point 180° around the origin is to change the sign of both numbers: $(x, y)$ becomes $(-x, -y)$. Think of this as flipping the point directly across the center to the opposite side.
3. Calculate:
* Change positive 3 to negative 3.
* Change positive 5 to negative 5.
* The new coordinate is $(-3, -5)$.

Correct Option: D

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Problem 3

Question: If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?

1. Find the starting coordinate: Just like in the previous problem, point $A$ is at $(3, 5)$.
2. Apply the rule: The rule for rotating 90° counterclockwise is to swap the numbers and make the first one negative: $(x, y)$ becomes $(-y, x)$.
* *Why?* Imagine the point is in the top-right corner. If you spin it 90° to the left (counterclockwise), it lands in the top-left corner. In the top-left, x is negative and y is positive.
3. Calculate:
* Take the y-value (5) and make it negative: $-5$. This is your new x-coordinate.
* Take the x-value (3) and keep it positive: $3$. This is your new y-coordinate.
* The new coordinate is $(-5, 3)$.

Correct Option: A

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Final Answer:
1. C
2. D
3. A