Answer:
The quadrilateral is a rhombus
Step-by-step explanation:
Given
![A = (2, 8)](https://tex.z-dn.net/?f=A%20%3D%20%282%2C%208%29)
![B = (3, 11)](https://tex.z-dn.net/?f=B%20%3D%20%283%2C%2011%29)
![C = (4, 8)](https://tex.z-dn.net/?f=C%20%3D%20%284%2C%208%29)
![D=(3, 5)](https://tex.z-dn.net/?f=D%3D%283%2C%205%29)
Required
The true statement
Calculate slope (m) using
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Calculate distance using:
![d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-y_1%29%5E2%7D)
Calculate slope and distance AB
![m_{AB} = \frac{11 - 8}{3 - 2}](https://tex.z-dn.net/?f=m_%7BAB%7D%20%3D%20%5Cfrac%7B11%20-%208%7D%7B3%20-%202%7D)
![m_{AB} = \frac{3}{1}](https://tex.z-dn.net/?f=m_%7BAB%7D%20%3D%20%5Cfrac%7B3%7D%7B1%7D)
-- slope
![d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}](https://tex.z-dn.net/?f=d_%7BAB%7D%3D%20%5Csqrt%7B%283%20-%202%29%5E2%20%2B%20%2811%20-8%29%5E2%7D)
-- distance
Calculate slope and distance BC
![m_{BC} = \frac{8 - 11}{4 - 3}](https://tex.z-dn.net/?f=m_%7BBC%7D%20%3D%20%5Cfrac%7B8%20-%2011%7D%7B4%20-%203%7D)
![m_{BC} = \frac{- 3}{1}](https://tex.z-dn.net/?f=m_%7BBC%7D%20%3D%20%5Cfrac%7B-%203%7D%7B1%7D)
-- slope
![d_{BC} = \sqrt{(4-3)^2+(8-11)^2](https://tex.z-dn.net/?f=d_%7BBC%7D%20%3D%20%5Csqrt%7B%284-3%29%5E2%2B%288-11%29%5E2)
--- distance
Calculate slope CD
![m_{CD} = \frac{5 - 8}{3 - 4}](https://tex.z-dn.net/?f=m_%7BCD%7D%20%3D%20%5Cfrac%7B5%20-%208%7D%7B3%20-%204%7D)
![m_{CD} = \frac{- 3}{- 1}](https://tex.z-dn.net/?f=m_%7BCD%7D%20%3D%20%5Cfrac%7B-%203%7D%7B-%201%7D)
-- slope
![d_{CD} = \sqrt{(3-4)^2+(5-8)^2}](https://tex.z-dn.net/?f=d_%7BCD%7D%20%3D%20%5Csqrt%7B%283-4%29%5E2%2B%285-8%29%5E2%7D)
-- distance
Calculate slope DA
![m_{DA} = \frac{8 - 5}{2 - 3}](https://tex.z-dn.net/?f=m_%7BDA%7D%20%3D%20%5Cfrac%7B8%20-%205%7D%7B2%20-%203%7D)
![m_{DA} = \frac{3}{- 1}](https://tex.z-dn.net/?f=m_%7BDA%7D%20%3D%20%5Cfrac%7B3%7D%7B-%201%7D)
-- slope
![d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}](https://tex.z-dn.net/?f=d_%7BDA%7D%20%3D%20%5Csqrt%7B%282-3%29%5E2%20%2B%20%288-5%29%5E2%7D)
![d_{DA} = \sqrt{10}](https://tex.z-dn.net/?f=d_%7BDA%7D%20%3D%20%5Csqrt%7B10%7D)
From the computations above, we can see that all 4 sides are equal, i.e. ![\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D)
And the slope of adjacent sides are negative reciprocal, i.e.
and ![m_{CD} = -3](https://tex.z-dn.net/?f=m_%7BCD%7D%20%3D%20-3)
and ![m_{DA} = -3](https://tex.z-dn.net/?f=m_%7BDA%7D%20%3D%20-3)
<em>The quadrilateral is a rhombus</em>
Answer:
Step-by-step explanation:
Line CP is a perpendicular bisector to line segment AB
if
two congruent lines are formed when AB is intersected ( bisector forms two equal in measure and congruent parts)
and
a right angle is formed between the line CP and AB ( perpendicular lines form right angles.)
![(2 \times {2}^{2} - 10) \times (2 + 9) = - 22](https://tex.z-dn.net/?f=%282%20%5Ctimes%20%20%7B2%7D%5E%7B2%7D%20%20-%2010%29%20%5Ctimes%20%282%20%20%2B%209%29%20%3D%20%20-%2022)
B
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Answer:
y= 0.8x
Step-by-step explanation:
Answer:
8/3
Step-by-step explanation:
Use ratios and the rule of three.
A : B
? : D
In this case you will always multiply D by A and divide it by B to find the unknown. Now just apply this to our question.
4/5 lbs : $3
? : $10
10 * 4/5 = 8
8÷3 = 8/3