Section 1
What is a Transformation?
Property
A geometric transformation is a function that maps each point of a figure, called the pre-image, to a new point in a figure called the image. We denote the image of a point as (read as "A prime").
In this Grade 8 lesson from Big Ideas Math Course 3, Chapter 2, students learn how to identify and perform translations in the coordinate plane by sliding figures without turning them, using the rule (x, y) → (x + a, y + b) to shift vertices horizontally and vertically. Students also explore how translations can be used to create tessellations, covering a plane with repeated congruent shapes and no gaps. The lesson connects coordinate geometry to real-world patterns while reinforcing the concept that translated figures are always congruent to the original.
Section 1
What is a Transformation?
A geometric transformation is a function that maps each point of a figure, called the pre-image, to a new point in a figure called the image. We denote the image of a point as (read as "A prime").
Section 2
Applying the Coordinate Rule for Translations
To apply a coordinate rule like (x, y) -> (x + a, y + b) and find the exact new location of a figure, you must mathematically substitute the coordinates of EACH vertex of the pre-image into the rule. By calculating (x + a) to find the new x-coordinate and (y + b) to find the new y-coordinate, you generate the exact coordinate points for the translated image, ensuring the shape remains perfectly congruent.
This is where students often stumble on basic integer math. Here are the micro-skills to double-check:
Section 3
Definition of Congruent Triangles
Two figures are congruent if and only if they have the exact same size and the exact same shape. We write to show that triangle is congruent to triangle .
Congruent figures are identical in every way except for their position in space. Think of congruent figures as exact clones of each other that can be moved around, flipped over, or turned without changing their inherent size or shape. When figures are congruent, every corresponding angle and side must be completely equal.
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Section 1
What is a Transformation?
A geometric transformation is a function that maps each point of a figure, called the pre-image, to a new point in a figure called the image. We denote the image of a point as (read as "A prime").
Section 2
Applying the Coordinate Rule for Translations
To apply a coordinate rule like (x, y) -> (x + a, y + b) and find the exact new location of a figure, you must mathematically substitute the coordinates of EACH vertex of the pre-image into the rule. By calculating (x + a) to find the new x-coordinate and (y + b) to find the new y-coordinate, you generate the exact coordinate points for the translated image, ensuring the shape remains perfectly congruent.
This is where students often stumble on basic integer math. Here are the micro-skills to double-check:
Section 3
Definition of Congruent Triangles
Two figures are congruent if and only if they have the exact same size and the exact same shape. We write to show that triangle is congruent to triangle .
Congruent figures are identical in every way except for their position in space. Think of congruent figures as exact clones of each other that can be moved around, flipped over, or turned without changing their inherent size or shape. When figures are congruent, every corresponding angle and side must be completely equal.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter