Mathematics, 25.09.2020 02:01 naomicervero

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?

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The length of MN and M'N' is 2 and 5 respectively and 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 than parallelogram MNPQ.

Given :

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.Points - M(2,-2), N(4,-2), P(3,-3), Q(1,-3)Points - M'(5,-5), N'(10,-5), P'(8,-7), Q'(3,-7)

A) First, find the length of MN:

$\rm |MN| = \sqrt{(4-2)^2+(-2-(-2))^2} =2$

Therefore, this option is correct.

B) Now, find the length of M'N':

$\rm |M'N'| = \sqrt{(10-5)^2+(-5-(-5))^2} =5$

Therefore, this option is correct.

C) 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 than parallelogram MNPQ. So the image is bigger than the pre-image. Therefore, this option is incorrect.

D) MQ slope is given by:

$\rm m_1 = \dfrac{1-2}{-3-(-2)}=1$

M'Q' slope is given by:

$\rm m_2= \dfrac{3-5}{-7-(-5)}=1$

So, the sides MQ and M'Q' both have the same slope, 1. Therefore, this option is correct.

E) 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 than parallelogram MNPQ. Therefore, this option is incorrect.

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Answer from: tori829

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

Answer from: Quest

Top right since it passes vertical line test
Which graph represents a function?

Answer from: Quest

step-by-step explanation:

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