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Gwar [14]
3 years ago
8

Describe a similarity transformation that maps △ABC

Mathematics
2 answers:
PIT_PIT [208]3 years ago
7 0

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

raketka [301]3 years ago
5 0

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.

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Answer:

8 yards < 10 yards

He has enough.

Step-by-step explanation:

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3 0
2 years ago
The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than
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Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

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15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

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5 + 38 + z = 80

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6 0
3 years ago
There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. Ho
Aleonysh [2.5K]
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3 years ago
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