Question

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) Responses h=1 and k=6 h equals 1 and k equals 6 h=−1 and k=6 h equals negative 1 and k equals 6 h=−1 and k=−6 h equals negative 1 and k equals negative 6 h=6 and k=−1

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 the translation that Mel applies to triangle ABC to reach triangle A'B'C'.

In the context of a translation in the coordinate plane:
- \( h \) represents the horizontal shift.
- \( k \) represents the vertical shift.

To identify \( h \) and \( k \), you'd typically look at the coordinates of a specific point before and after the translation. For example, if point A has coordinates \( (x_1, y_1) \) before translation, and point A' has coordinates \( (x_1 + h, y_1 + k) \) after translation, then:
- \( h = x' - x \)
- \( k = y' - y \)

Without the actual coordinates or a specific scenario given, we cannot directly determine the values of \( h \) and \( k \).

However, let’s analyze the response options given. The only way to correctly identify \( h \) and \( k \) from the options would be by knowing the translation vector or having the coordinates before and after.

If you have the specific coordinates of points A, B, C and their corresponding translated points A', B', C', please provide them, and I can calculate the values of \( h \) and \( k \) for you.