Question

Jacinda 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. A is (-5,1) B is (-3,4) C is (-4,-2) A' is (0,2) B' is (2,5) C' is (1,-1) What are the values of h and k in these functions?(1 point)The value of h is and the value of k is .

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 find the changes in the x-coordinates and y-coordinates as triangle ABC is translated to triangle A'B'C'.

1. Finding \( h \) (Change in x-coordinates):

   • For point A:
     • Original A: \((-5, 1)\)
     • Translated A': \((0, 2)\)
   • The change in the x-coordinate from A to A' is: \[ 0 - (-5) = 0 + 5 = 5 \]
   • Therefore, \( h = 5 \).

2. Finding \( k \) (Change in y-coordinates):

   • For point A:
   • The change in the y-coordinate from A to A' is: \[ 2 - 1 = 1 \]
   • Therefore, \( k = 1 \).

In summary, the values are:

• \( h = 5 \)
• \( k = 1 \)

So, the final answer is:

• The value of \( h \) is 5 and the value of \( k \) is 1.