6.3: Compositions | Geometry Honors | Code Scholars Tutoring

How it works

Apply coordinate transformations in the stated order. Function composition acts from right to left. Reversing a translation and a reflection can change the image, so show the intermediate point.

(F\circ T)(P)=F(T(P))

Worked examples

Example 1

Translate $\displaystyle (1,2)$ by $\displaystyle (3,0)$ , then reflect across the $\displaystyle y$ -axis.

Translation gives $\displaystyle (4,2)$ ; reflection gives $\displaystyle (-4,2)$ .

Example 2

Reverse the operations in the preceding example.

Reflection first gives $\displaystyle (-1,2)$ ; translation then gives $\displaystyle (2,2)$ . The results differ.

Problems

Problem 6.3.1

Apply a $\displaystyle 90^\circ$ counterclockwise rotation about the origin twice to $\displaystyle (3,1)$ .

Show worked solution

First $\displaystyle (-1,3)$ , then $\displaystyle (-3,-1)$ . The composition is a $\displaystyle 180^\circ$ rotation.

Problem 6.3.2

Reflect $\displaystyle (2,5)$ across the $\displaystyle x$ -axis and then the $\displaystyle y$ -axis.

Show worked solution

The intermediate point is $\displaystyle (2,-5)$ and the final point is $\displaystyle (-2,-5)$ .

Problem 6.3.3

Translate a point by $\displaystyle (4,-2)$ and then by $\displaystyle (-1,5)$ . Give the single equivalent translation.

Show worked solution

Add displacement vectors: $\displaystyle (3,3)$ .

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 6.3.1

Problem 6.3.2

Problem 6.3.3

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