Respuesta :
Answer:
The answer is C) (5.7, 2.2)
Step-by-step explanation:
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Coordinates of the point M of the given line segment with given partition is equals to ( 5.7, 2.2) ( nearest tenth).
What is section formula?
" Section formula is defined as the coordinates which divides the line segment with given endpoints in the predefine ratio."
Formula used
Section formula
M (x, y) divides line segment with coordinates [tex]K( x_{1} ,y_{1} ) , N( x_{2} ,y_{2} )[/tex] in the ratio m:n.
Coordinates of M(x, y) = [tex](\frac{mx_{2} + nx_{1} }{m+n} , \frac{my_{2} + ny_{1} }{m+n} )[/tex]
According to the question,
Coordinates of K (x₁ , y₁) = ( -6, -2)
Coordinates of N(x₂ , y₂) = (8, 3)
L(x, y) divides the line segment from K to N in a ratio 1 : 2.
Substitute the value in the section formula to get the coordinates ,
L( x, y) = [ {(1 )(8) + (2) (-6)} / ( 1+ 2) , (1 )(3) + (2) (-2)] / ( 1+ 2)]
= [(8 - 12 ) / 3 , (3 - 4) / 3]
= (- 4 / 3 , -1 / 3)
M(x, y) divides the line segment from L to N in a ratio 3 : 1
Substitute the value in the section formula to get the coordinates ,
M( x, y) = [ {(3 )(8) + (1) (-4/3)} / ( 3+ 1) , (3 )(3) + (1) (-1/3)] / ( 3+ 1)]
= ( 17/3 , 26 / 12)
= ( 5.666... , 2.1666..)
= ( 5.7 , 2.2) (nearest tenth)
Hence, coordinates of the point M of the given line segment with given partition is equals to ( 5.7, 2.2) ( nearest tenth).
Learn more about section formula here
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