All categories

3 years ago

(Image shown below this of the shape)

Mathematics

1 answer:

omeli [17]3 years ago

5 0

Answer:

a) A reduction

b) The scale factor is 1/2

Step-by-step explanation:

The vertices of the original figure, ABCD are;

A(-2, 4), B(4, 4), C(2, -2), and D(-4, -2)

The vertices of the image, A'B'C'D' are;

A'(-1, 2), B'(2, 2), C'(1, -1), and D'(-2, -1)

a) The length of the side AB = 4 - (-2) = 6 (Distance between points having the same 'x' or 'y' coordinates

The length of the side A'B' = 2 - (-1) = 3

The length of AB = 6 is larger than the length of A'B' = 3, therefore the image A'B'C'D' is a reduction of (is smaller) the figure ABCD

b) The scale factor = The ratio of the lengths corresponding sides of the image to the original figure;

∴ The scale factor =A'B'/AB = A'D'/AD = B'C'/BC = D'C'/DC

AD = √((-4 - (-2))² + (-2 - 4)²) = 2·√10

A'D' = √((-2 - (-1))² + (-1 - 2)²) = √10

A'D'/AD= √10/(2·√10) = 1/2

Therefore, given that the coordinates of the preimage are 2 × the coordinates of the image, we have;

The scale factor = A'B'/AB = B'C'/BC = D'C'/DC = A'D'/AD =1/2

The scale factor is 1/2, therefore, we multiply the dimensions of the original figure by 1/2 to get the dimensions of the image.

The scale factor = 1/2.

You might be interested in

Which methods will determine 70% of 42?

Dennis_Churaev [7]

Answer:

Step-by-step explanation:

Given

(3x + 7)(2x - 6)

Each term in the second factor is multiplied by each term in the first factor, that is

3x(2x - 6) + 7(2x - 6) ← distribute both parenthesis

= 6x² - 18x + 14x - 42 ← collect like terms

= 6x² - 4x - 42 → C

5 0

3 years ago

Read 2 more answers

Kareem purchased a leather jacket for $800 with his new credit card. He budgeted $50 a month to pay toward the debt. When he rea

barxatty [35]

Answer:

1080

Step-by-step explanation:

Firstly, if he is paying 50 per month, we need to know the number of months it would take him to finish paying the money. Hence that would be 800/50 = 16 months

Now we know there is a surcharge of 17.5 for each month he owes a balance. The total balance he is to pay is thus 16 * 17.5 = 280

The total cost of the jacket is thus 800 + 280 = 1080

6 0

4 years ago

The residence of a city voted on whether to raise property taxes the ratio of yes votes to know votes was 5 to 6 if there was 58

Akimi4 [234]

5/6:x/5844

Cross multiply to get
29220=6x
x=4870

4870+5844=

10714 votes

Hope this helped :)

7 0

2 years ago

Sally is ordering lunch at a cafeteria. She has 3 choices for her salad, 2 choices for the main course, 4 choices for dessert an

Shkiper50 [21]

Hello there,

Your correct answer would be 72. Because 3x2x4x3= 72

I Hope this helps you!

~Jurgen

6 0

4 years ago

Read 2 more answers

Miguel collected aluminum cans for recycling. He collected a total of 150 cans. If 58% of the cans he collected were soda cans h

Romashka-Z-Leto [24]

Given:

• Total number of cans collected = 150

• Percent of cans that were soda = 58%

Let's find the number of other cans he collected.

To find the number of other cans, since the percent of soda is 58%, let's find the pecent of other cans.

Percent of other cans = 100% - 58% = 42%

The percent of other cans collected was 42%.

Now, to find the number of other cans collected, let's find 42% of the total number of cans collected 150.

We have:

$42\text{ \% }\ast150\Longrightarrow0.42\times150=63$

Therefore, the number of other cans collected is 63 cans.

ANSWER:

63 cans

4 0

1 year ago