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Naddika [18.5K]

3 years ago

14

A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ afte

r a 180° rotation about the origin and a translation 5 units to the right and 1 unit down?

1 answer:

Ivahew [28]3 years ago

8 0

Answer:

$A'(4,-2)$ $B'(0,-5)$ $C'(-2,-2)$ $D'(2,1)$

Step-by-step explanation:

The given parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2).

The rotation of $180\degree$ about the origin has the mapping;

$P(x,y)\rightarrow P'(-x,-y)$

This implies that;

$A(1,1)\rightarrow (-1,-1)$

$B(5,4)\rightarrow (-5,-4)$

$C(7,1)\rightarrow (-7,-1)$

$D(3,-2)\rightarrow (-3,2)$

A translation of 5 units to the right and 1 unit down has the mapping;

$P(x,y)\rightarrow P'(x+5,y-1)$

We apply this to the resulting coordinates to obtain;

$A(1,1)\rightarrow (-1,-1) \rightarrow (-1+5,-1-1)=A'(4,-2)$

$B(5,4)\rightarrow (-5,-1) \rightarrow (-5+5,-4-1)=B'(0,-5)$

$C(7,1)\rightarrow (-7,-1)\rightarrow (-7+5,-1-1)=C'(-2,-2)$

$D(3,-2)\rightarrow (-3,2)\rightarrow (-3+5,2-1)=D'(2,1)$

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Answer:

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Step-by-step explanation:

To find the length of the line AB, we just need to find the distance between the points A and B.

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To find the equation of the line BC, first let's find the slope of the line AB.

This slope is given by:

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so the line BC is:

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Step-by-step explanation:

This a probability problem.

The probability formula is given by:

$P = \frac{D}{T}$

In which P is the probability, D is the number of desired outcomes and T is the number of total outcomes.

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121 people walked by the store.

66 people came into the store.

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There is a 55% probability that a person who walks by the store will enter the store.

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$D = 25, T = 66$

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There is a 38% probability that a person who walks into the store will buy something.

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$P = \frac{D}{T} = \frac{25}{121} = 0.21$

There is a 21% probability that a person who walks by the store will come in and buy something.

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$D = 41, T = 66$

$P = \frac{D}{T} = \frac{41}{66} = 0.62$

There is a 62% probability that a person who comes into the store will buy nothing.

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