Adding the same number 'k' to both coordinates of (7, 8) maintains the proportionality, preserving the ratio of 7:8 in the updated coordinates (7 + k, 8 + k). Adele is correct.
Let's break it down step by step:
1. Given Point: The point is (7, 8). This implies a ratio of 7:8, where 7 is the x-coordinate and 8 is the y-coordinate.
2. Add the Same Number (k): Let's add the same number 'k' to both coordinates. The new coordinates become (7 + k, 8 + k).
3. New Coordinates: These new coordinates, (7 + k, 8 + k), represent the updated values after adding 'k' to both x and y.
4. Equivalent Ratio: The new ratio formed by the updated coordinates is (7 + k):(8 + k). This is equivalent to the original ratio of 7:8.
5. Explanation: Adele's claim is valid because by adding the same number 'k' to both coordinates, we maintain proportionality. The ratio between the x and y coordinates remains consistent, and the overall relationship between the numbers is preserved.
In summary, Adele is correct, and the addition of the same number to both coordinates results in an equivalent ratio.