Answer:
Step-by-step explanation:
<h3>To prove quadrilateral is a square:</h3>
a) Slope of CB
C(-3,-1) ; B = (0,3)
![\sf = \dfrac{3-[-1]}{0-[-3]}\\\\ =\dfrac{3+1}{0+3}\\\\ = \dfrac{4}{3}](https://tex.z-dn.net/?f=%5Csf%20%3D%20%5Cdfrac%7B3-%5B-1%5D%7D%7B0-%5B-3%5D%7D%5C%5C%5C%5C%20%3D%5Cdfrac%7B3%2B1%7D%7B0%2B3%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B4%7D%7B3%7D)
b) D(1,-4) ; A(4,0)
![Slope \ of \ DA = \dfrac{0-[-4]}{4-1}\\](https://tex.z-dn.net/?f=Slope%20%5C%20of%20%5C%20DA%20%3D%20%5Cdfrac%7B0-%5B-4%5D%7D%7B4-1%7D%5C%5C)
Slope of CB = slope of DA
c) C(-3,-1) ; D(1 , -4)
![\sf Slope \ of \ CD =\dfrac{-4-[-1]}{1-[-3]}](https://tex.z-dn.net/?f=%5Csf%20Slope%20%5C%20of%20%5C%20CD%20%3D%5Cdfrac%7B-4-%5B-1%5D%7D%7B1-%5B-3%5D%7D)
So, CD is perpendicular to CB
d) B(0,3) ; D(1,-4)
e) C(-3,-1) ; A(4,0)
![\sf Slope \ of \ CA = \dfrac{0-[-1]}{4-[-3]}\\](https://tex.z-dn.net/?f=%5Csf%20Slope%20%5C%20of%20%5C%20CA%20%3D%20%5Cdfrac%7B0-%5B-1%5D%7D%7B4-%5B-3%5D%7D%5C%5C)
So, CA is perpendicular to BD
Answer:
Step-by-step explanation:
If the 2 is an exponent, it needs to be written as ^2.
(5+√3)² = 5² + 10√3 + 3 = 28 + 10√3
Answer:
Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.
So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"
Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.
We can select 3 vertices from 7 vertices in 7C3 ways.
Answer:
y would be 6
Step-by-step explanation:
Because 5 x 3 would be 15
then you would do 2 x 3 would be 6
