Transformation Introduction

Front

What is a transformation in geometry?

Back

A transformation in geometry refers to the movement of a shape or point in a coordinate plane, which can include translations, rotations, reflections, and dilations.

Front

What does it mean to translate a point?

Back

To translate a point means to move it from one location to another in the coordinate plane without changing its shape or orientation.

Front

How do you perform a translation of a point?

Back

To perform a translation, you add specific values to the x-coordinate and y-coordinate of the point. For example, translating a point (x, y) by (a, b) results in the new point (x+a, y+b).

Front

What are the coordinates of point J if it is translated 5 units left and 2 units up from (0, 5)?

Back

The new coordinates of point J would be (-5, 7).

Front

What is the result of translating the point (3, 4) 3 units to the right and 2 units down?

Back

The new coordinates would be (6, 2).

Front

What is the significance of the origin in a coordinate plane?

Back

The origin is the point (0, 0) in a coordinate plane, where the x-axis and y-axis intersect. It serves as the reference point for all other points.

Front

How do you identify the coordinates of a point in a coordinate plane?

Back

The coordinates of a point are identified as (x, y), where 'x' represents the horizontal distance from the origin and 'y' represents the vertical distance from the origin.

Front

What does it mean to reflect a point across the x-axis?

Back

Reflecting a point across the x-axis means to invert the y-coordinate of the point while keeping the x-coordinate the same. For example, the reflection of (3, 4) is (3, -4).

Front

What is the effect of a reflection across the y-axis on the coordinates of a point?

Back

Reflecting a point across the y-axis means to invert the x-coordinate of the point while keeping the y-coordinate the same. For example, the reflection of (3, 4) is (-3, 4).

Front

What is a rotation in geometry?

Back

A rotation in geometry is a transformation that turns a shape or point around a fixed point, known as the center of rotation, by a certain angle.