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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

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

Step-by-step 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

step-by-step explanation: