Mel draws triangle ABC and translates it along the coordinate grid to produce triangle A′B′C′. Then, he determines the functions f(x)=x+h and g(y)=y+k that describe the translation. What are the values of h and k in these functions? (1 point)

Question

Responses
h=−1 and k=6
h=6 and k=−1
h=−1 and k=−6
6 h=1 and k=6

Answer 1

To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to understand how translations work in the coordinate plane.

• If the triangle is translated to the right, \( h \) will be positive.
• If the triangle is translated to the left, \( h \) will be negative.
• If the triangle is translated upwards, \( k \) will be positive.
• If the triangle is translated downwards, \( k \) will be negative.

To find the specific values of \( h \) and \( k \), we would need the original coordinates of points \( A, B, C \) and their translated coordinates \( A', B', C' \) after the translation.

However, since specific coordinates are not given, we can analyze the options provided for \( h \) and \( k \):

1. \( h = -1 \) and \( k = 6 \)
2. \( h = 6 \) and \( k = -1 \)
3. \( h = -1 \) and \( k = -6 \)
4. \( h = 1 \) and \( k = 6 \)

If you know the direction of the translation (for example, triangle A moves left by 1 and upwards by 6), you can select the corresponding option.

If any additional information about the translation is provided, please share it, and we can find the correct values of \( h \) and \( k \) together!