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Mel draws triangle ABC and translates it along the coordinate grid to produce triangle A'B'C'. Then, he determines the function f (x) = x + h and g (y) = y + k that describe the translation. What are the values of h and k in these functions?

a. h = 6 and k = -1
b. h = -1 and k = 6
c. h = 1 and k = 6
d. h = -1 and k = -6

1 answer

To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \), we need information about how the triangle is translated.

In a translation, points of the original triangle are moved to new coordinates based on the values of \( h \) and \( k \):

  • If \( h \) is positive, the triangle moves to the right; if \( h \) is negative, it moves to the left.
  • If \( k \) is positive, the triangle moves up; if \( k \) is negative, it moves down.

Without specific information about the original coordinates of triangle \( ABC \) and the coordinates of triangle \( A'B'C' \), we cannot definitively determine the values of \( h \) and \( k \) from the choices provided.

To solve this problem, you would generally check the translation distance by comparing corresponding points in triangles \( ABC \) and \( A'B'C' \):

  1. Identify the coordinates of points \( A \), \( B \), and \( C \) (the original triangle).
  2. Identify the coordinates of points \( A' \), \( B' \), and \( C' \) (the translated triangle).
  3. Calculate \( h = x' - x \) for one point (using the x-coordinates of any corresponding points).
  4. Calculate \( k = y' - y \) for the same point (using the y-coordinates).
  5. Determine which of the answer choices matches the calculated values of \( h \) and \( k \).

If you have specific coordinates for triangles \( ABC \) and \( A'B'C' \), please provide them so we can find \( h \) and \( k \) together.