1) Write a translation rule that maps point D(7, –3) onto point D'(2, 5).
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To find the translation rule that maps point D(7, -3) onto point D'(2, 5), we need to determine the horizontal and vertical shifts needed to move from D to D'.
The horizontal shift can be found by calculating the difference between the x-coordinates of D' and D. In this case, the x-coordinate of D' is 2 and the x-coordinate of D is 7. Thus, the horizontal shift is given by:
Horizontal Shift = x-coordinate of D' - x-coordinate of D
= 2 - 7
= -5
The vertical shift can be found by calculating the difference between the y-coordinates of D' and D. In this case, the y-coordinate of D' is 5 and the y-coordinate of D is -3. Thus, the vertical shift is given by:
Vertical Shift = y-coordinate of D' - y-coordinate of D
= 5 - (-3)
= 5 + 3
= 8
Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is a horizontal shift of -5 units and a vertical shift of 8 units.
Translation Rule: (x, y) -> (x - 5, y + 8)