Respuesta :
Answer:
a) ( 3 , 6 )
b) y = -2*x / 3 + 7
Step-by-step explanation:
Given:
- The four points are:
(-9,13), (-3, 9), (3, 6) and (9, 1)
- Three points lie on the same line.
Find:
Which one of the four points does not lie on the same line as the other three?
Solution:
- Compute the slope between each pair of point:
(-9,13), (-3, 9)
m_1 = ( 9 - 13 ) / ( -3 + 9 ) = - 2/3
(-9,13), (3, 6)
m_2 = ( 6 - 13 ) / ( 3 + 9 ) = - 0.5833
(-9,13), (9, 1)
m_3 = ( 1 - 13 ) / ( 9 + 9 ) = - 2/3
- We see that m_1 = m_3 ≠ m_2 . Hence, point ( 3 ,6 ) does not lie on the same line.
- The equation of line is expressed as:
y = m*x + C
m = -2/3
y = -2*x / 3 + C
1 = -2*9 / 3 + C ....... ( 9 , 1 )
C = 7
- The equation of the line is:
y = -2*x / 3 + 7
Points A(-9, 13), B(-3, 9) and D(9, 1) are colinear.
b). Equation of the line passing through these points will be [tex]y=-\frac{2}{3}x+7[/tex]
Property for the colinear points:
- If three points are colinear, slope of the lines joining these points will be equal.
- Slope of a line joining two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given points in the question,
A(-9, 13), B(-3, 9), C(3, 6) and D(9, 1)
If the slopes of the lines joining these points are same, points will be colinear.
Slope of AB = [tex]\frac{13-9}{-9+3}=-\frac{2}{3}[/tex]
Slope of AC = [tex]\frac{13-6}{-9-3}=-\frac{7}{12}[/tex]
Slope of AD = [tex]\frac{13-1}{-9-9}=-\frac{2}{3}[/tex]
Since, slopes of AB and AD are equal, points A, B and D will be colinear.
b). Let the equation of the line passing through A, B and D is,
y - y' = m(x - x')
Since, this line passes through D(9, 1) and slope = [tex]-\frac{2}{3}[/tex]
Equation of the line → [tex]y-1=-\frac{2}{3}(x-9)[/tex]
[tex]y=-\frac{2}{3}x+6+1[/tex]
[tex]y=-\frac{2}{3}x+7[/tex]
Therefore, points A(-9, 13), B(-3, 9) and D(9, 1) are colinear and equation of the line passing through these points will be [tex]y=-\frac{2}{3}x+7[/tex].
Learn more about the slope of a line here,
https://brainly.com/question/490077?referrer=searchResults
