Question

Question

Use the image to answer the question.

A coordinate plane shows two points upper A and upper A prime plotted in quadrant 2 and quadrant 1, respectively. Both axes range from negative 5 to 5 in increments of 1.

On this coordinate plane, point A
is translated into point A′
. Which functions give the two translations?

(1 point)
Responses

f(x)=x+6
and g(y)=y+3
f left parenthesis x right parenthesis equals x plus 6 and g left parenthesis y right parenthesis equals y plus 3

f(x)=x+5
and g(y)=y+2
f left parenthesis x right parenthesis equals x plus 5 and g left parenthesis y right parenthesis equals y plus 2

f(x)=x+2
and g(y)=y+5
f left parenthesis x right parenthesis equals x plus 2 and g left parenthesis y right parenthesis equals y plus 5

f(x)=x−5
and g(y)=y−2

Answer 1

To determine the correct translations for the points A and A', we need to identify their coordinates based on the description provided.

Assuming point A is in quadrant 2 (where x is negative and y is positive) and point A' is in quadrant 1 (where both x and y are positive), we can analyze the given options by looking at how the coordinates of A translate into the coordinates of A'.

Let's denote the coordinates of point A as (x_A, y_A) and the coordinates of point A' as (x_A', y_A').

Given that translations happen through functions f(x) and g(y):

1. The translation for the x-coordinate can be represented as: \( f(x) = x + c_x \) where \( c_x \) is the amount added to the x-coordinate during translation.

2. The translation for the y-coordinate can be represented as: \( g(y) = y + c_y \) where \( c_y \) is the amount added to the y-coordinate during translation.

Let's look at the provided options:

1. Option 1: \( f(x) = x + 6 \) and \( g(y) = y + 3 \)
2. Option 2: \( f(x) = x + 5 \) and \( g(y) = y + 2 \)
3. Option 3: \( f(x) = x + 2 \) and \( g(y) = y + 5 \)
4. Option 4: \( f(x) = x - 5 \) and \( g(y) = y - 2 \)

You'll need to analyze the translation based on the specific coordinates of A and A'. If you determine the correct shifts needed for the x and y coordinates based on their starting and ending coordinates, you can match them to the equations in the options.

If you find that point A's x-coordinate needs to increase by 5 and its y-coordinate needs to increase by 2 to reach point A', then the answer would be option 2.

Without the specific coordinates, it's difficult to determine the exact answer. If you have the coordinates, simply examine each option to see which functions correctly describe the translations.