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

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

h=−1
and k=6
h equals negative 1 and k equals 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 know the specific translation that triangle ABC underwent to become triangle A′B′C′.

The parameters \( h \) and \( k \) represent the horizontal and vertical shifts, respectively:

- \( h \) indicates how much to translate triangle ABC horizontally (to the right if positive, to the left if negative).
- \( k \) indicates how much to translate triangle ABC vertically (upwards if positive, downwards if negative).

Without knowing the coordinates of the original triangle ABC and the translated triangle A′B′C′, it's impossible to determine the correct values of \( h \) and \( k \).

Could you provide the coordinates of the vertices (points) of triangles ABC and A′B′C′ for a complete and accurate analysis?