Final answer:
To find the image of the point (20,70) under a translation that moves (5,10) to (9,2), we add 4 units to the x-coordinate and subtract 8 units from the y-coordinate, resulting in new coordinates (24,62).
Step-by-step explanation:
Understanding Translations in Coordinate Geometry
When a translation moves a point (5,10) to a new position (9,2), we can determine this translation's effect on any other point in the same coordinate plane. To do this, we calculate the difference between the x-coordinates and the y-coordinates of the original and translated points. In this case, the x-coordinate has increased by 4 units (9 - 5), and the y-coordinate has decreased by 8 units (2 - 10).
To apply this same translation to another point, such as (20,70), we add 4 units to the x-coordinate and subtract 8 units from the y-coordinate. Therefore, the image of the point (20,70) under this translation will be (20 + 4, 70 - 8) which gives us the new coordinates (24,62).