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Points C open parentheses negative 5 comma 8 close parentheses and D open parentheses 2 comma 5 close parentheses lie on line C D. If points C apostrophe and D apostrophe are created by translating points C and D left 6 units, what is the slope of line C apostrophe D apostrophe ?

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We want to find the slope of the line that connects points C' and D'. We will find that the slope is -3/7.

First, we start with the points:

  • C = (-5, 8)
  • D = (2, 5)

Now we create points C' and D' by translating points C and D to the left by 6 units, this means that we need to subtract 6 in the x-value of each point, so we will have:

  • C' = (-5, 8) + (-6, 0) = (-5 - 6, 8) = (-11, 8)
  • D' = (2, 5) + (-6, 0) = (2 - 6, 5) = (-4, 5)

And we know that if a line passes through points (x₁, y₁) and (x₂, y₂) the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Then the slope that connects points C' and D' is:

[tex]a = \frac{5 - 8}{2 - (-5)} = \frac{-3}{7}[/tex]

If you want to learn more, you can read:

https://brainly.com/question/2263981

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