Transformations in Geometry

Questions and Answers

What are the coordinates of the point (−4, 2) after a translation 2 units left and 2 units up?

(-6, 4)

A sequence of transformations that maps △ABC to △A′B′C′ is a _ followed by a __.

rotation of 90° counterclockwise, translation 2 units right

What are the new coordinates of the triangle after the transformation with the rule (x, y)→(−x, y)?

(-3, 4), (-4, 7), (-8, 2)

What are the new coordinates of the triangle after the transformation with the rule (x, y)→(x−6, y−4)?

<p>(-4, 1), (0, -2), (-3, -9)</p> Signup and view all the answers

What sequence of transformations maps △ABC to △A′B′C′?

<p>Reflection across the y-axis, Translation 2 units left</p> Signup and view all the answers

Study Notes

Translations and Transformations

After translating the point (−4, 2) by moving 2 units left and 2 units up, the new coordinates become (−6, 4).

Sequences of Transformations

To map triangle △ABC to triangle △A′B′C′, apply a rotation of 90° counterclockwise followed by a translation of 2 units to the right.

Triangular Transformation Rules

For the transformation rule (x, y) → (−x, y), the new coordinates from points (-3, 4), (-4, 7), and (-8, 2) are formed by flipping them over the y-axis.
When applying the transformation (x, y) → (x−6, y−4), the vertices (-4, 6), (-2, 2), and (-6, 2) are shifted down and left, resulting in new coordinates (-4, 1), (0, -2), and (-3, -9).

Vertex Coordinates

The vertices of triangle △ABC are A(−4, 6), B(−2, 2), and C(−6, 2).
The transformed vertices of triangle △A′B′C′ are A′(2, 6), B′(0, 2), and C′(4, 2).
Mapping through a reflection across the y-axis and a translation of 2 units left transitions triangle △ABC to △A′B′C′.

Description

This quiz explores the various types of transformations in geometry, including translations, rotations, and reflections. You'll apply these concepts to find new coordinates of points and triangles after specific transformations. Test your understanding of how these transformations affect geometric shapes and their properties.