Question

on this coordinate plane, point a is translated into point a. which functions give the two translations? (1 point) f(x)=x + 2 and g(y)=y + 5 f(x)=x + 6 and g(y)=y + 3 f(x)=x - 5 and g(y)=y - 2 f(x)=x - 7 and g(y)=y - 2

Explanation:

Step1: Determine the coordinates of point A

The coordinates of point A are $(-2,3)$.

Step2: Assume the coordinates of point A'

Let's assume we need to find the translation rules. If we assume point A' has coordinates $(x_1,y_1)$ after translation. For a translation in the x - direction, the rule for the x - coordinate of a point $(x,y)$ is $x'=x + a$ (where $a$ is the horizontal translation), and for the y - direction is $y'=y + b$ (where $b$ is the vertical translation).

Step3: Analyze the translation options

We need to check each option. For example, if $f(x)=x + 2$ and $g(y)=y+5$, for point $A(-2,3)$:
The new x - coordinate after applying $f(x)$ is $x=-2 + 2=0$, and the new y - coordinate after applying $g(y)$ is $y=3 + 5 = 8$.
If $f(x)=x + 6$ and $g(y)=y + 3$, for point $A(-2,3)$:
The new x - coordinate is $x=-2+6 = 4$, and the new y - coordinate is $y=3 + 3=6$.
If $f(x)=x - 5$ and $g(y)=y - 2$, for point $A(-2,3)$:
The new x - coordinate is $x=-2-5=-7$, and the new y - coordinate is $y=3 - 2 = 1$.
If $f(x)=x+4$ and $g(y)=y - 2$, for point $A(-2,3)$:
The new x - coordinate is $x=-2 + 4=2$, and the new y - coordinate is $y=3-2 = 1$.

However, since the options are not fully visible in the image, assume the correct translation from the visible part. If we assume the correct horizontal translation is $x'=x + 4$ and vertical translation is $y'=y - 2$ (by counting the grid - squares of translation from A to A' if A' is known).

Answer:

The correct functions for the translation (assuming the correct option is $f(x)=x + 4$ and $g(y)=y - 2$ based on the general concept of translation) are the ones that correctly move the point $A(-2,3)$ to the coordinates of $A'$. But from the visible options, if we assume the correct one based on the general rule of translation, if the translation is 4 units to the right and 2 units down, the functions are $f(x)=x + 4$ and $g(y)=y - 2$ (but this answer depends on the actual position of $A'$ which is not fully clear from the given image). If we had to choose from the visible options in a more complete scenario, we would calculate the new coordinates for each option as shown above and pick the one that matches the actual position of $A'$.