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?

Question

a. 4
b. -10
c. 0
d. 10

Answer 1

To find the value of \( k \) in the function \( g(y) = y + k \) that describes the translation from the point \( (5, -3) \) to the point \( (5, 7) \), we can follow these steps:

1. Identify the original and final coordinates:

   • Original coordinate: \( y = -3 \)
   • Final coordinate: \( y = 7 \)

2. The translation function can be expressed as: \[ g(y) = y + k \]

3. We want to find \( k \) such that when we translate \( y = -3 \), we get \( 7 \): \[ g(-3) = -3 + k = 7 \]

4. To solve for \( k \), we can rearrange this equation: \[ -3 + k = 7 \] \[ k = 7 + 3 \] \[ k = 10 \]

So the value of \( k \) is \( 10 \).

Thus, the answer is d. 10.