Question
A point is translated on the coordinate plane from (5, -3) to (5,7). Journey write the function g(y)= y + k to describe the translation. What is the value of k?
a. 0
b. 10
c. 4
d. -10
a. 0
b. 10
c. 4
d. -10
Answers
GPT-4o mini
To find the value of \( k \) in the function \( g(y) = y + k \) that describes the translation of the point \( (5, -3) \) to \( (5, 7) \), we can observe the change in the \( y \)-coordinates.
The initial \( y \)-coordinate is \( -3 \) and the final \( y \)-coordinate is \( 7 \).
The translation can be described by the change in \( y \):
\[
\text{Change in } y = 7 - (-3) = 7 + 3 = 10
\]
Thus, the function \( g(y) \) that describes this translation will be:
\[
g(y) = y + 10
\]
This means \( k = 10 \).
Therefore, the value of \( k \) is \( \text{b. } 10 \).
The initial \( y \)-coordinate is \( -3 \) and the final \( y \)-coordinate is \( 7 \).
The translation can be described by the change in \( y \):
\[
\text{Change in } y = 7 - (-3) = 7 + 3 = 10
\]
Thus, the function \( g(y) \) that describes this translation will be:
\[
g(y) = y + 10
\]
This means \( k = 10 \).
Therefore, the value of \( k \) is \( \text{b. } 10 \).