Final answer:
a. For the points (2,6) and (-6, -8), Ax = -8 - 6 = -14 and Ay = -6 - 2 = -8.
b. Considering (0,9) and (4, -8), Ax = -8 - 9 = -17 and Ay = 4 - 0 = 4.
c. With (-3, -3) and (7, 10), Ax = 10 - (-3) = 13 and Ay = 7 - (-3) = 10.
Step-by-step explanation:
To find the components Ax and Ay between two points (x₁, y₁) and (x₂, y₂), the horizontal (Ax) and vertical (Ay) changes between the points need to be calculated. The formula to compute Ax is the difference between the x-coordinates of the points (x₂ - x₁), and Ay is the difference between their y-coordinates (y₂ - y₁).
For instance, in case (a) for points (2,6) and (-6, -8), Ax = x₂ - x₁ = -6 - 2 = -8 - 6 = -14 and Ay = y₂ - y₁ = -8 - 6 = -14. In (b) with (0,9) and (4, -8), Ax = x₂ - x₁ = 4 - 0 = 4 and Ay = y₂ - y₁ = -8 - 9 = -17. Lastly, in (c) with (-3, -3) and (7, 10), Ax = x₂ - x₁ = 7 - (-3) = 10 and Ay = y₂ - y₁ = 10 - (-3) = 13.
These components Ax and Ay denote the changes in the x and y directions between the given pairs of points. Ax represents the horizontal change (rightward or leftward), while Ay signifies the vertical change (upward or downward) when moving from one point to the other. These values are essential in various mathematical contexts, such as vector calculations and analyzing motion in physics or geometry.