Question

Dianna draws triangle ABC and translates it along the coordinate grid to produce triangle A′B′C′ . Then, she 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=8 and k=−5 h equals 8 and k equals negative 5 h=5 and k=−8 h equals 5 and k equals negative 8 h=2 and k=−5 h equals 2 and k equals negative 5 h=−8 and k=−5
A=(-7,4) B=(-3,0) C=(-1,4)
A'=(1,-1) B'=(5,-5) C'(7,-1)

Answer 1

To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \) for the translation from triangle ABC to triangle A'B'C', we need to analyze the coordinates of points A, B, and C compared to A', B', and C'.

The coordinates of triangle ABC are:
- A = (-7, 4)
- B = (-3, 0)
- C = (-1, 4)

The coordinates of triangle A'B'C' are:
- A' = (1, -1)
- B' = (5, -5)
- C' = (7, -1)

### Finding \( h \)
To find \( h \), we can compare the \( x \)-coordinates of points A and A':
\[
1 = -7 + h \\
h = 1 + 7 \\
h = 8
\]

### Finding \( k \)
Now for \( k \), we can compare the \( y \)-coordinates of points A and A':
\[
-1 = 4 + k \\
k = -1 - 4 \\
k = -5
\]

Thus, the values are:
- \( h = 8 \)
- \( k = -5 \)

So the answer is:
**h = 8 and k = −5**