Respuesta :
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:
[tex]|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[/tex]
The first option is correct
b) The length of side M'N' is determined using the formula:
[tex]|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[/tex]
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:
[tex]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\\[/tex]
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
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:
[tex]\rm |MN| = \sqrt{(4-2)^2+(-2-(-2))^2} =2[/tex]
Therefore, this option is correct.
B) Now, find the length of M'N':
[tex]\rm |M'N'| = \sqrt{(10-5)^2+(-5-(-5))^2} =5[/tex]
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:
[tex]\rm m_1 = \dfrac{1-2}{-3-(-2)}=1[/tex]
M'Q' slope is given by:
[tex]\rm m_2= \dfrac{3-5}{-7-(-5)}=1[/tex]
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.
For more information, refer to the link given below:
https://brainly.com/question/19187374
