Composition of Transformations Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard

Triangle

ABC

with

A(1,0)

B(3,0)

C(2,2)

is rotated

90°

counterclockwise about the origin, then reflected over the

y

-axis. Find the final vertices.

Solution

1
Rule for $90°$ CCW rotation: $(x,y) \to (-y, x)$ . Apply: $A(1,0)\to A'(0,1)$ , $B(3,0)\to B'(0,3)$ , $C(2,2)\to C'(-2,2)$ .
2
Rule for reflection over the $y$ -axis: $(x,y)\to(-x,y)$ . Apply: $A'(0,1)\to A''(0,1)$ , $B'(0,3)\to B''(0,3)$ , $C'(-2,2)\to C''(2,2)$ .
3
The final triangle has vertices $A''(0,1)$ , $B''(0,3)$ , $C''(2,2)$ .

Answer

A''(0,1)

B''(0,3)

C''(2,2)

Compositions of rigid transformations preserve shape and size. Applying coordinate rules step-by-step ensures accuracy. Note that

A''

and

B''

lie on the

y

-axis because the rotation moved them there and the reflection fixed those points.

About Composition of Transformations

Composition of transformations applies two or more transformations in sequence to a figure, where the output of one transformation becomes the input of the next. The order matters because transformation composition is generally not commutative.

Learn more about Composition of Transformations →

More Composition of Transformations Examples

Example 1 medium

Point [formula] is first reflected over the [formula]-axis, then translated by vector [formula]. Fin

Example 3 easy

Point [formula] is translated by [formula] and then reflected over the [formula]-axis. Find the fina

Example 4 medium

Describe the single transformation equivalent to two successive reflections over parallel lines [for

← All Composition of Transformations Examples Composition of Transformations Concept

Related Concepts

Translation Rotation Reflection