Question

Consider the following points A(-2,20) and P(10.-13).

AP undergoes the translation such that A'(-28,37) and
P'(-16,4). Write the algebraic description as a function rule.

Answer 1

The translation vector for the transformation from points A to A' and P to P' is (-26, 17), yielding the function rule T(x, y) = (x - 26, y + 17).

Step-by-step explanation:

The question involves finding the algebraic description or the function rule for a translation of points A and P to A' and P'. We begin by finding the change in x and y coordinates separately. To find the translation vector, we subtract the original coordinates of point A from the translated coordinates A'. Similarly, we do the same for point P to P'. Calculating A', we get:

• Δx = x2 - x1 = (-28) - (-2) = -26
• Δy = y2 - y1 = 37 - 20 = 17

For point P', we get:

• Δx = x2 - x1 = (-16) - (10) = -26
• Δy = y2 - y1 = 4 - (-13) = 17

Since both points A and P have the same change in the x and y directions, we can determine the translation vector to be (-26, 17). Therefore, the algebraic description for the translation is:

T(x, y) = (x - 26, y + 17)