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#3 y^(')(2,-4) is the image of y after a translation along the rule (x,y)rarr(x-4,y-3). What are the coordinates of pre-image y ?

\#33 y′(2,−4) y^{\prime}(2,-4) is the image of y y after a translation along the rule (x,y)→(x−4,y−3) (x, y) \rightarrow(x-4, y-3) . What are the coordinates of pre-image y y ?

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Q. \#33 y′(2,−4) y^{\prime}(2,-4) is the image of y y after a translation along the rule (x,y)→(x−4,y−3) (x, y) \rightarrow(x-4, y-3) . What are the coordinates of pre-image y y ?
  1. Reverse Translation Rule: To find the pre-image coordinates, we need to reverse the translation rule. The translation rule given is (x,y)→(x−4,y−3)(x, y) \rightarrow (x - 4, y - 3). To reverse this, we add 44 to the xx-coordinate and add 33 to the yy-coordinate of the image point.
  2. Calculate Original X-coordinate: The image point is y′(2,−4)y'(2, -4). To find the pre-image yy, we calculate the original x-coordinate by adding 44 to the image's x-coordinate: 2+42 + 4.
  3. Calculate Original Y-coordinate: The calculation for the x-coordinate of the pre-image is 2+4=62 + 4 = 6.
  4. Calculate Pre-image Coordinates: Next, we calculate the original yy-coordinate by adding 33 to the image's yy-coordinate: −4+3-4 + 3.
  5. Calculate Pre-image Coordinates: Next, we calculate the original yy-coordinate by adding 33 to the image's yy-coordinate: −4+3-4 + 3.The calculation for the yy-coordinate of the pre-image is −4+3=−1-4 + 3 = -1.

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