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Schach [20]
3 years ago
10

a line segment has (x1,y1) as one endpoint and (xm,ym) as its midpoint. Find the other endpoint (x2,y2)of the line segment in te

rms of x1,y1,xm, and ym.
Mathematics
2 answers:
svlad2 [7]3 years ago
7 0

(x1,y1)

(x2,y2)

(xm,ym)

Midpoint formula is given as below.

((x1 + x2)/2 , (y1 + y2)/2 )

Where

(x1 + x2)/2 = xm ----------- (1)

(y1 + y2)/2 = ym ----------- (2)

Equation (1) implies that;

x1 + x2 = 2xm

x2 = 2xm – x1

Equation (2) implies that;

y1 + y2 = 2ym

y2 = 2ym – y1

Thus the end point is

<span>(x2,y2) = (2xm – x1, 2ym – y1)</span>

Neko [114]3 years ago
7 0
<span>A line segment has (x1, y1)as one endpoint and (xm, ym)as its midpoint.

Use the formula? (x2, y2) = (2xm − x1, 2ym − y1) to find the coordinates of the endpoint of a line segment if the coordinates of the other endpoint and midpoint are (1, 8), (−3, −1) and (−7, 16), (3, 6),respectively.
 
(a) Endpoint: (1, 8), (−3, −1) (x2, y2) = ( , )
(b) Midpoint: (−7, 16), (3, 6) (x2, y2) = ( , )
           

ANSWER a) (x2,y2) = (2x-x1, 2y-y1) for midpoints m = 1 = {(2(-3)-1), (2(-1)-8)} = (-7,-10)

Answer  b) (x2,y2) = (2x-x1, 2y-y1) for midpoints m = 1 = {(2(3)+7), (2(6)+16)} = (13,28)</span>
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Answer:

a)Slope: \hat \beta_1 =\frac{7625.9}{1248.9}=6.106

Intercept: \hat \beta_o = 157.955 -6.106 (69.686)=-267.548

b) r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"    

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

\sum Y_i =17375 , \sum X_i = 7665.5

Part a

The slope is given by this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

If we replace we got:

\hat \beta_1 =\frac{7625.9}{1248.9}=6.106

We can find the intercept with the following formula

\hat \beta_o = \bar y -\hat \beta_1 \bar x

We can find the average for x and y like this:

\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955

And replacing we got:

\hat \beta_o = 157.955 -6.106 (69.686)=-267.548

Part b

In order to calculate the correlation coefficient we can use this formula:  

r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}  

For our case we have this:  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

So we can find the correlation coefficient replacing like this:

r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

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