contestada

Describe a similarity transformation that maps △ABC
to △RST

A(6, 4), B(−2, 0), C(−4, 2)and R(2, 3), S(0,−1), T(1,−2)

Fill in the blanks below. Please show all the work on how you got your answer.

Describe a similarity transformation that maps ABC to RST A6 4 B2 0 C4 2and R2 3 S01 T12 Fill in the blanks below Please show all the work on how you got your a class=

Respuesta :

DeanR

Let's start with a picture.

We see RST is smaller, and BC is parallel to but in the opposite direction to its corresponding segment ST.  Both have slope -1.

If we look at the difference of points (technically called vectors but we don't have to go there) we get

C-B=(-2,2)

T-S=(1,-1)

Without further calculation we can see T-S is half the length of C-B.

The problem asks for a dilation followed by a reflection.   We know the dilation scale is k=1/2 because the new triangle is half the size.  

After dilation we get A'B'C':

A'(3,2), B'(-1,0), C'(-2,1)

We see now we need a reflection that flips the coordinates x and y.  That's the +45° line through the origin, namely y=x.

Answer: k=1/2, y=x

sqdancefan

Answer:

  see second attachment

Step-by-step explanation:

ΔRST is smaller, so the scale factor must be less than 1. The only available answer choice is k = 1/2.

When you scale ΔABC by 1/2, you get A'(3, 2), B'(-1, 0), C'(-2, 1). Comparing these coordinates to R, S, T, we find the x-, and y-values are swapped. This indicates a reflection across the line y=x.

____

In the graph, ΔA'B'C' is purple, ΔRST is blue.

Ver imagen sqdancefan
Ver imagen sqdancefan

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