Question

2. Here is triangle ABC drawn on a grid.

A
B
с
On the grid, draw a rotation
of triangle ABC, a
translation of triangle ABC,
and a reflection of triangle
ABC. Describe clearly how
each was done. (please help, thanks!!)

Answer 1

Greetings from Brasil...

Let's place the triangle in a Cartesian Plane - see attached figure.

We have:

A(1; 2)

B(3; 1)

C(6; 3)

1 - rotation

Specifically for a 90° rotation, we will use the expression

A(X; Y) → A'(-Y; X)

then

A'(-2; 1)

B'(-1; 3)

C'(-3; 6)

2 - translation

For a translation, we will add n units in all coordinates. (instead of adding, we could too subtract)

A(X; Y) → A''(X + n; Y + n)

Let's consider n = 2, so

A''(3; 4)

B''(5; 3)

C''(8; 5)

3 - reflection

No way. We have to draw the original figure and reflect it. Let's use the Y axis as the reflection axis.

See the attachments

Answer 2

See attachments.

Explanation:

Rotation, translation and reflection are all examples of transformations A transformation is a way by which the size or position of a shape is changed.

Rotation

(See attachment 1)

Rotation turns a shape around a fixed point called the center of rotation.

• Choose a center of rotation: the center of the grid.
• Decide upon an angle of rotation: 90°.
• Decide upon a direction of rotation: clockwise.
• Draw lines from each point of the triangle to the center of rotation.
• Rotate the lines 90° clockwise.
• Place points at the ends of the rotated lines.
• Join the points to create the rotated shape.

Translation

(See attachment 2)

A translation moves a shape left, right, up or down.

Every point on the original shape is translated (moved) the same distance in the same direction.

• Choose a translation: 2 units to the left and 3 units down.
• Translate (move) each point of the original image by the defined translation.
• Place points.
• Join the points to create the translated shape.

Reflection

(See attachment 3)

A shape can be reflected across a line of reflection.

Every point on the reflected shape is the same distance from the line of reflection as the corresponding points on the original shape.

The lines joining the points on the original shape and the corresponding points on the reflected shape are perpendicular to the line of reflection.

• Choose a line of reflection: horizontal center-line.
• Draw a vertical line (perpendicular to the line of reflection) from each point on the original shape.
• Extend the line so that it is twice the length.
• Place corresponding points at the end of the lines.
• Join the points to create the reflected shape.

Summary

All three transformations have been drawn on one grid in attachment 4.