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

Question

On this coordinate plane, point B
is translated to point B′
. Which functions describe the two translations?

(1 point)
Responses

f(x)=x−5
and g(y)=y+3
f left parenthesis x right parenthesis equals x minus 5 and g left parenthesis y right parenthesis equals y plus 3

f(x)=x−2
and g(y)=y+6
f left parenthesis x right parenthesis equals x minus 2 and g left parenthesis y right parenthesis equals y plus 6

f(x)=x+6
and g(y)=y−2
f left parenthesis x right parenthesis equals x plus 6 and g left parenthesis y right parenthesis equals y minus 2

f(x)=x−6
and g(y)=y+2

Answer 1

To determine which functions describe the translations from point B to point B', it's essential to know the coordinates of both points before evaluating the options.

Here's the general process:

1. Identify Coordinates: First, identify the coordinates of points B and B'.
2. Determine the Translation: Determine how the x-coordinate and y-coordinate change from B to B'.
3. Select the Right Functions: Using the translation determined in Step 2, identify which functions correspond to those translations.

Since the specific coordinates of points B and B' are not provided in your question, I will guide you through this process if you have the coordinates:

• If point B has coordinates (x_B, y_B) and point B' has coordinates (x_B', y_B'), you can express the translations as:
  • For the x-coordinate:
    • \( f(x) = x + (x_B' - x_B) \)
  • For the y-coordinate:
    • \( g(y) = y + (y_B' - y_B) \)

After calculating the changes in x and y coordinates, look at the provided functions and see which one matches your translations:

1. f(x) = x - 5, g(y) = y + 3
2. f(x) = x - 2, g(y) = y + 6
3. f(x) = x + 6, g(y) = y - 2
4. f(x) = x - 6, g(y) = y + 2

If you can provide the coordinates of points B and B', I can help determine the correct translation functions.