6.6.1. Rao (page 368, 1973) considers a problem in the estimation of linkages in genetics. McLachlan and Krishnan (1997) also di

scuss this problem and we present their model. For our purposes, it can be described as a multinomial model with the four categories C1, C2, C3 , and C4 . For a sample of size n, let X = (X1, X2, X3 , X4 )′ denote the observed frequencies of the four categories. Hence, n = +4 i=1 Xi. The probability model is

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Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3). Round your answer to the ne

tester [12383]

Answer: 20 units

Step-by-step explanation:

The formula for calculating the distance between two coordinates P(a,b) and Q(c,d) is as follows:-

$PQ=\sqrt{(d-b)^2+(c-a)^2}$

Initially provided: The coordinates of the quadrilateral's vertices are C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

The distance between vertices C (−2, 1) and D (2, 4) is as follows:-

$CD=\sqrt{(4-1)^2+(2-(-2))^2}\\\\\Rightarrow\ CD=\sqrt{(3)^2+(4)^2}\\\\\Rightarrow\ CD=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ CD=5\text{ units}$

Distance between points D (2, 4) and E (5, 0) is calculated as:-

$DE=\sqrt{(4-0)^2+(2-5)^2}\\\\\Rightarrow\ DE=\sqrt{(4)^2+(-3)^2}\\\\\Rightarrow\ DE=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ DE=5\text{ units}$

Distance between coordinates E (5, 0) and F (1, −3) is given by:-

$EF=\sqrt{(-3-0)^2+(1-5)^2}\\\\\Rightarrow\ EF=\sqrt{(-3)^2+(-4)^2}\\\\\Rightarrow\ EF=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ EF=5\text{ units}$

Distance from C (−2, 1) to F (1, −3) is as follows:-

$FC=\sqrt{(-3-1))^2+(1-(-2))^2}\\\\\Rightarrow\ FC=\sqrt{(-4)^2+(3)^2}\\\\\Rightarrow\ FC=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ FC=5\text{ units}$

The total perimeter of the quadrilateral is calculated as = CD + DE + EF + FC

$=5+5+5+5=20\text{ units}$

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