Question

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'. On a coordinate plane, 2 parallelograms are shown. Parallelogram M N P Q has points (2, negative 2), (4, negative 2), (3, negative 3), and (1, negative 3). Parallelogram M prime N prime P prime Q prime has points (5, negative 5), (10, negative 5), (8, negative 7), and (3, negative 7). Which statements are true about the parallelograms?

Answer 1

Answer:

1,2, and 4 or a,b, and d

Step-by-step explanation:

i got it on edge! ; )

Answer 2

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