Angle relationships worksheet #2 10-17

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'. On a coordinate plane, 2 parallelograms are shown. Parallelogra

Naddika [18.5K]

Answer:

The answer is below

Step-by-step explanation:

Which statements are true about the parallelograms? Check all that apply.

The length of side MN is 2 units.

The length of side M'N' is 5 units.

The image is smaller than the pre-image.

Sides MQ and M'Q' both have the same slope, 1.

The scale factor is 2/5

a) The length of side MN is determined using the formula:

$|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-2)^2+(-2-(-2))^2}=\sqrt{2^2}=2\\ \\ |MN|=2$

The first option is correct

b) The length of side M'N' is determined using the formula:

$|M'N'|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(10-5)^2+(-5-(-5))^2}=\sqrt{5^2}=2\\ \\ |M'N'|=5$

The second option is correct

c) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q' , hence parallelogram M'N'P'Q' is bigger that parallelogram MNPQ. This means that The image is bigger than the pre-image.

The third option is wrong

d) The slopes are given as:

$Slope\ of\ MQ=\frac{Change\ in\ y}{Change\ in\ x}=\frac{1-2}{-3-(-2)} =1\\ \\Slope\ of\ M'Q'=\frac{Change\ in\ y}{Change\ in\ x}=\frac{3-5}{-7-(-5)} =1\\$

Option four is correct

e) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence the scale factor is 5/2

Option 5 is wrong

6 0

3 years ago

Read 2 more answers

Find the missing side

Verdich [7]

Answer:

$x=15.56$

Step-by-step explanation:

We can use the law of sines here. However, we will first need to solve for the missing angle.

The interior angles of a triangle add up to 180.

Therefore,

$35+90+x=180$

where $x$ is the missing angle.

$35+90+x=180$

$x+125=180$

$x=55$

So the missing angle is 55 degrees.

Now we can use the law of sines to set up a proportion.

$\frac{19}{sin(90)}=\frac{x}{sin(55)}$

Now simplify the equation.

$x=15.56$

<em>Rounded to the nearest hundredth.</em>

8 0

3 years ago

Read 2 more answers

Nia has number cards 2,3,8,9, and 5 . What are the different way bus can arrange the cards to show only even numbers with 2 in t

kodGreya [7K]

If i'm not mistaken there is only 10 or 25 ways he could arrange them,
ie: 23,895, 28395, ect....

5 0

4 years ago

An insurance agent earns a base salary of $28,000, a commission of 2% of sales, and receives an additional fee of $9 for each sa

Murrr4er [49]

Answer:

$54 for fees

$1500 for commission

$29554 in total

Step-by-step explanation:

They will have $28000 regardless.

The commission is 2% so you multiply 0.02 (which is equivalent to 2%) to $75000, so he earns $1500. He sold 6 sales so he you multiply 6 by $9 and you get $54.

I don't know exactly what your asking but

$54 for fees

$1500 for commission

$29554 in total

4 0

3 years ago

Acell divides into 2 cells every min. Calculate the number of cells after 10 min.

Rainbow [258]

Answer:

20

Step-by-step explanation:

2 cells per minute

and ten minutes of it

so ...10 x 2

8 0

3 years ago