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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. A is at 2, 2 and a' is at 1, -3

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 determine the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to find how the coordinates of point \( A \) translate to point \( A' \).

The coordinates of point \( A \) are \( (2, 2) \) and the coordinates of point \( A' \) are \( (1, -3) \).

To find \( h \) and \( k \):

1. For the \( x \)-coordinate: \[ A_x + h = A'_x \] \[ 2 + h = 1 \] Solving for \( h \): \[ h = 1 - 2 = -1 \]

2. For the \( y \)-coordinate: \[ A_y + k = A'_y \] \[ 2 + k = -3 \] Solving for \( k \): \[ k = -3 - 2 = -5 \]

Therefore, the values are:

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