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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...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)
A=(-7,4) B=(-3,0) C=(-1,4)
A'=(1,-1) B'=(5,-5) C'(7,-1)
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GPT-4o mini
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**
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**
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