13. Write a translation rule that maps point D(7, –3) onto point D'(2, 5).
14. Triangle ABC has coordinates A(1, 4); B(3, –2); and C(4, 2). Find the coordinates of the image A'B'C' after a reflection over the x-axis
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To write a translation rule that maps point D(7, -3) onto point D'(2, 5), we need to find the difference in x and y coordinates between the two points.
The x-coordinate difference is: x' - x = 2 - 7 = -5
The y-coordinate difference is: y' - y = 5 - (-3) = 8
Therefore, the translation rule is (x, y) -> (x - 5, y + 8).
Now, let's move on to the second question.
To find the coordinates of the image A'B'C' after a reflection over the x-axis, we need to reflect each point individually.
For point A(1, 4), when we reflect over the x-axis, the x-coordinate stays the same, but the y-coordinate becomes its negative value. Therefore, the image A' is (1, -4).
For point B(3, -2), the image B' will also have the same x-coordinate, but its y-coordinate will be the negative value of the original. So, B' is (3, 2).
Similarly, for point C(4, 2), the image C' will have the same x-coordinate and the negative y-coordinate. Therefore, C' is (4, -2).
Thus, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1, -4), B'(3, 2), and C'(4, -2).