Respuesta :
Answer:
The correct option is 3.
Step-by-step explanation:
It is provided that:
A number line goes from negative 5 to positive 10.
Point D is at negative 2, i.e. Point D = -2.
Point F is at positive 7, i.e. Point F = 7.
A line is drawn from point D to point F.
Point G divides the directed line segment from D to F into a 5 : 4 ratio.
Consider the diagram below.
The distance between the points D and F is of 9 units (from -2 to 7).
If Point G divides the directed line segment from D to F into a 5 : 4 ratio, then the point G must be located at 3.
Thus, the correct option is 3.
At the location of point, G is 2, which partitions the directed line segment from D to F into a 5:4 ratio.
Given that,
A number line goes from negative 5 to positive 10.
Point D is at negative 2 and point F is at positive 7.
A line is drawn from point D to point F.
We have to determine,
What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio?
According to the question,
A number line goes from negative 5 to positive 10.
Point D is at negative 2 and point F is at positive 7.
The distance between point D and F is,
[tex]=\sqrt{(7-(-2))^2}\\\\= \sqrt{(9^2)}\\\\= 9[/tex]
If Point G divides the directed line segment from D to F into a 5: 4 ratio, then,
[tex]\dfrac{ G-F}{D-G} = \dfrac{5}{4}\\\\4(G-F) = 5(D-G)\\\\4G -4F = 5D-5G\\\\ 9G = 5D +4F \\\\ G =\dfrac{ 5D +4F}{9} \\\\ G = \dfrac{5(-2) +4(7)}{9}\\\\G =\dfrac{ (-10 +28)}{9} \\\\G = \dfrac{18}{9}\\\\ G = 2[/tex]
Hence, At the location of point G is 2, which partitions the directed line segment from D to F into a 5:4 ratio.
To know more about Geometry click the link given below.
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