Point M is 4.2 cm from centre C. After a rotation of -60° about C, what is the distance CM' and in which direction is the angle measured from line segment CM?

Grade 10 · Core Mathematics · Lesson 3 of 13

Rotating Shapes on a Plane Surface

A Grade 10 Core Mathematics CBE lesson from the sub-strand Rotation. In it, learners identify the centre of rotation, angle of rotation, and direction of turn on a plane surface.

Strand Measurements and GeometrySub-strand RotationLesson code 10CM-23-L340 minutes · 3 slides

KICD learning outcome (b)

Rotate an object given the centre and angle of rotation on a plane surface and the Cartesian plane.

By the end of this lesson, learners should be able to

Identify the centre of rotation, angle of rotation, and direction of turn on a plane surface.
Rotate a single point on a plane surface about a given centre through a specified angle.
Rotate 2D shapes on a plane surface vertex by vertex using geometric construction tools.

Key vocabulary

Centre of rotation: The fixed point around which an object or point is turned during a rotation.; Point O is the centre of rotation for turning point P through fifty degrees.
Angle of rotation: The amount and direction of turning around a fixed centre point during rotation.; The angle of rotation is positive fifty degrees in the anticlockwise direction.
Anticlockwise: The direction of rotation opposite to the movement of clock hands, representing positive angles.; Angle VX V prime is measured in the anticlockwise direction for plus forty-five degrees.
Image vertex: The new position of a vertex after undergoing a geometric transformation such as rotation.; Point E prime is the image vertex formed by rotating vertex E about centre O.

Lesson preview

Slide 1 · Rotating a Single Point on a Plane SurfaceOpening · 12 min

A point P is rotated about a fixed centre O through a designated angle to locate its corresponding image point P'. — Figure 1: A point $P$ is rotated about a fixed centre $O$ through a designated angle to locate its corresponding image point $P^{'}$ .

To rotate a given point about a fixed centre through a designated angle on a plane surface, construct a straight line segment connecting the point to the pivot. With a protractor, measure the turn angle from this segment at the pivot point, drawing a ray. A positive angle indicates an anticlockwise turn, while a negative angle indicates a clockwise turn. Finally, mark the image point along the ray at a distance from the centre equal to that of the original point.

A rotation on a plane surface requires a fixed centre point and a turn angle.
Connect each given point to the rotation centre using a straight line segment.
Measure the specified turn angle at the centre point using a protractor in the proper direction.
Mark the image point such that its distance from the pivot matches the original point.

Worked example. Connect point

P

to the centre of rotation

O

to form line segment

O P = 5 cm

. Place a protractor at

O

with baseline on

O P

and measure an angle of

50^{\circ}

in the anticlockwise direction. Draw a ray from

O

passing through the

50^{\circ}

mark. Mark image point

P^{'}

along this ray such that

O P^{'} = O P = 5 cm

. Answer: Point $P^{'}$ lies on the ray at angle $+ 50^{\circ}$ from segment $O P$ , at distance $O P^{'} = 5 cm$ from centre $O$ ..

Check question: Point $M$ is $4.2 cm$ from centre $C$ . After a rotation of $- 60^{\circ}$ about $C$ , what is the distance $C M^{'}$ and in which direction is the angle measured from line segment $C M$ ?

$C M^{'} = 4.2 cm$ , measured clockwise
$C M^{'} = 4.2 cm$ , measured anticlockwise
$C M^{'} = - 4.2 cm$ , measured clockwise
$C M^{'} = - 4.2 cm$ , measured anticlockwise

Show answer

$C M^{'} = 4.2 cm$ , measured clockwise. Rotation preserves the distance from the pivot point, so $C M^{'} = C M = 4.2 cm$ . A negative rotation angle of $- 60^{\circ}$ means turning in the clockwise direction.

Slide 2 · Rotating a Triangle About a Centre PointModel · 14 min

A triangle is rotated anticlockwise about a centre point X by moving vertex V to locate the corresponding image vertex V'. — Figure 2: A triangle is rotated anticlockwise about a centre point $X$ by moving vertex $V$ to locate the corresponding image vertex $V^{'}$ .

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This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

All 3 slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 12 lessons in this sub-strand

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Rotating Shapes on a Plane Surface

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 13 lessons in Rotation