Find the slope of each line.

A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following tra

olga55 [171]

The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;

a. A'(4, 6), B'(10, 8), C'(6, 12)

b. A'(-2, -2), B'(4, 0), C'(0, 4)

c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)

The area of dilation 1 and 2 are the same
The center of dilation does not change the area

d. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1

The angle measures are the same

<h3>How can the new coordinates be found?</h3>

The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;

$D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))$

Where;

(a, b) = The center of dilation

k = The scale factor of dilation

(x, y) = The coordinate of the pre-image

The given points are;

A(2, 3), B(5, 4), C(3, 6)

a. The scale factor of dilation = 2

The center of dilation = The origin (0, 0)

Therefore;

$D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)$

Therefore dilation about the origin, with a scale factor of 2 gives;

A(2, 3) → A'(4, 6)

Similarly

B(5, 4) → B'(10, 8)

C(3, 6) → C'(6, 12)

b. With the center of dilation at (6, 8), we have;

$D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)$

A(2, 3) → A'(-2, -2)

$D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)$

B(5, 4) → B'(4, 0)

$D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)$

C(3, 6) → C'(0, 4)

c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places

Using notation, we have;

Dilation 1 T(-6, -8) → Dilation 2

The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.

The location of the center of dilation does not change the area of the image

d. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the <em>x </em>and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;

The proportion of the side lengths is 1

Given that the side lengths are the same, by AAA congruency postulate, we have;

The angle measures are the same.

Learn more about dilation transformation here:

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6 0

2 years ago

Read 2 more answers

Thanks in advance for your help

densk [106]

Answer:

CA=P+2Q

Step-by-step explanation:

7 0

2 years ago

Find the sum of 2 1/9 + (-2/9) + 3 5/9

polet [3.4K]

Answer:

5.444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

Step-by-step explanation:

4 is infinite

7 0

3 years ago

Read 2 more answers

What is a stem and leaf plot? How is it used and how exactly do i solve one? (an example would be great)

Ludmilka [50]

A stem and leaf plot is a table where each of the data is divided into two parts. The stem, that is the first digit and the leaf is the last digits. Let's say that we have the following set of data.

$10,\text{ 12, 25, 28, 29, 35, 38, 40, 44}$

If we want to make a stem and leaf plot of that data, we first write a column where we place the first digit of each number without repetition, like this:

$\begin{gathered} 1 \\ 2 \\ 3 \\ 4 \end{gathered}$

These are the stems. Now the leaves are the last digit of each number put in order next to the corresponding first digit, like this:

$\begin{gathered} 1\parallel\text{ 0 2} \\ 2\parallel\text{ 5 8 9} \\ 3\text{ }\parallel\text{5 8} \\ 4\text{ }\parallel\text{0 4} \end{gathered}$

8 0

1 year ago

Pls help me, is very important! Many thanks

Ber [7]

The inequality should be
$\times \leqslant 3$

8 0

3 years ago