If the line is shifted 10 units right side and 5 units downward side. Then the equation of the line is y + 8 = 0.
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Line segment FG begins at (-1, 5) and ends at (-1, -3). The segment is translated right 10 units and down 5 units to form line segment F'G'. Then the coordinate of F' and G' will be
F' = (-1 + 10, 5 - 5) = (9, 0)
G' = (-1 + 10, -3 - 5) = (9, -8)
Then the equation of the line passing through F' and G' will be
[tex]\rm y + 8 = \dfrac{-8-0}{9-9}(x - 9)\\\\y + 8 = 0[/tex]
More about the coordinate geometry link is given below.
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