Respuesta :
Answer:
The points where E' and F' are located after dilation and how the lines g and g' are related are;
The locations E' and F' are E'(-8, 0) and F'(0, 4), and lines g and g' are parallel
Please see attached plot of lines g and g' created with MS Excel
Step-by-step explanation:
When an object is dilated by a scale factor, the length of the sides of the image formed is given as follows;
The length of the image = The length of the figure × The scale factor
The given parameters are;
The center of dilation = (0, 0) Dilated from the origin
The coordinates of the endpoint of the line 'g' = E(-4, 0), F(0, 2)
Therefore, we have;
The 'x', and 'y' coordinates of the point E' on the image from the center of dilation (0, 0) = (-4 × 2, 0 × 2) = (-8, 0)
The 'x', and 'y' coordinates of the point F' on the image from the center of dilation (0, 0) = (0 × 2, 2 × 2) = (0, 4)
Therefore, the coordinates of the point E' and F' on line g' = E'(-8, 0) and F'(0, 4)
Given that the proportion of the distances of E and E' to center of dilation (to the origin) and F and F' center of dilation are equal by the triangle proportionality theorem, EF is parallel to E'F' and the lines g and g' are said to be parallel
Therefore;
The coordinate of point E' = (-8, 0) and The coordinate of point F' = (0, 4)
Ling g is parallel to line g'
Answer:
The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' are parallel.
Step-by-step explanation:
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