What are the coordinates of C', the image of C(5, -2), if it is reflected over the y-axis and then translated 5 units to the right and 3 units down?
Question
What are the coordinates of C', the image of C(5, -2), if it is reflected over the y-axis and then translated 5 units to the right and 3 units down?
Solution 1
Step 1: Reflect over the y-axis When a point is reflected over the y-axis, the x-coordinate changes its sign. So, the image of C(5, -2) after reflection over the y-axis is C'(-5, -2).
Step 2: Translate 5 units to the right and 3 units down When a point is translated to the right, the x-coordinate increases by the number of units moved. When a point is translated down, the y-coordinate decreases by the number of units moved. So, the image of C'(-5, -2) after translation is C'(-5+5, -2-3) = C'(0, -5).
So, the coordinates of C' after reflection over the y-axis and translation are (0, -5).
Solution 2
Step 1: Reflect over the y-axis When a point is reflected over the y-axis, the x-coordinate changes its sign. So, the image of C(5, -2) after reflection over the y-axis is C'(-5, -2).
Step 2: Translate 5 units to the right and 3 units down When a point is translated to the right, the x-coordinate increases. When a point is translated down, the y-coordinate decreases. So, the image of C'(-5, -2) after translation is C'(-5+5, -2-3) = C'(0, -5).
So, the coordinates of C' are (0, -5).
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