The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Write a translation rule that maps point D(7, −3)D(7, -3) onto point D'(2, 5).D'(2, 5).
To write a translation rule that maps point D(7,-3) onto point D'(2,5), we need to determine the horizontal and vertical shifts.
Translation is a type of transformation that moves every point in a figure the same distance and direction. In this case, we want to move point D(7,-3) to point D'(2,5).
To find the horizontal shift, we subtract the x-coordinates of D' and D:
Horizontal Shift = x-coordinate of D' - x-coordinate of D
Horizontal Shift = 2 - 7 = -5
To find the vertical shift, we subtract the y-coordinates of D' and D:
Vertical Shift = y-coordinate of D' - y-coordinate of D
Vertical Shift = 5 - (-3) = 8
Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:
(x, y) → (x - 5, y + 8)
This rule states that to map any point (x, y) to its corresponding point after translation, subtract 5 from the x-coordinate and add 8 to the y-coordinate.