Question

A coordinate plane shows two points upper A and upper A prime plotted in quadrant 1 and quadrant 4, respectively. Both axes range from negative 5 to 5 in increments of 1.

Image Long DescriptionPoint upper A is plotted at left parenthesis 2 comma 2 right parenthesis, and point upper A prime is plotted at left parenthesis 1 comma negative 3 right parenthesis. The coordinates are unlabeled.

Point A
on the coordinate plane is translated to point A′
, as shown. What are the values of h and k in the translation functions f(x)=x+h
and g(y)=y+k
?

(1 point)
The value of h is
and the value of k is
.

Answer 1

To find the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to determine how the coordinates of point \( A \) (2, 2) change to become the coordinates of point \( A' \) (1, -3).

1. **Finding \( h \)**:
\[
\text{Original x-coordinate of } A = 2
\]
\[
\text{New x-coordinate of } A' = 1
\]
To find \( h \):
\[
1 = 2 + h \implies h = 1 - 2 \implies h = -1
\]

2. **Finding \( k \)**:
\[
\text{Original y-coordinate of } A = 2
\]
\[
\text{New y-coordinate of } A' = -3
\]
To find \( k \):
\[
-3 = 2 + k \implies k = -3 - 2 \implies k = -5
\]

So the values are:
- The value of \( h \) is **-1**.
- The value of \( k \) is **-5**.