Question

Drag and drop the answers into the boxes to correctly complete the statement.

A sequence of transformations that maps △RST to △R′S′T′ is a _____ followed by a _____

A. reflection across the x-axis
B. Translation 1 unit down
C. Reflection across the y-axis
D. Rotation of 180 degrees about the origin

Answer 1

A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down

Explanation:

step 1

Find out the reflection of △RST across the x-axis

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

we have

R(1,3),S(1,1),T(4,1)

Applying the rule of reflection across the x-axis

R(1,3) -----> R''(1,-3)

S(1,1) -----> S''(1,-1)

T(4,1) ----> T''(4,-1)

step 2

Find out the translation of △R''S''T'' 1 unit down

The rule of the translation is

(x,y) -----> (x,y-1)

Applying the rule of the translation

R''(1,-3)-----> R'(1,-3-1)

R''(1,-3)-----> R'(1,-4)

S''(1,-1)----> S'(1,-1-1)

S''(1,-1)----> S'(1,-2)

T''(4,-1) ----> T'(4,-1-1)

T''(4,-1) ----> T'(4,-2)

therefore

A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down