Points A (2; 2) and B (8; 18) are given. Find the coordinates of points C and D if you know that point B

Points A (2; 2) and B (8; 18) are given. Find the coordinates of points C and D if you know that point B is the midpoint of segment AC, and point D is the midpoint of segment BC.

Given:
A (2; 2);
B (8; 18);
B – middle of AC;
D – middle of BC.
Find: coordinates C and D.
Decision:
Let’s start with the fact that the coordinates of point B are the arithmetic mean of the coordinates of two points A and C.
Based on this, we will compose the equation:
2 * B (8; 18) = A (2; 2) + C (x; y).
Next, we transform the equation by removing the point designations from it and multiplying B by 2. Then we get:
(16; 36) = (2; 2) + (x; y).
Then we move the numerical coordinates to the left, and leave only the unknown variables on the right.
(14; 34) = (x; y).
From here we get the coordinates of the point C. They are equal to C (14; 34).
Next, we will look for the coordinates of point D. Based on the condition, it is clear that this point is the arithmetic mean of two points B and C.
Also, as above, create an equation.
D (x; y) = 1/2 * (B (8; 18) + C (14; 34)).
Let’s do the action in brackets and get D (x; y) = 1/2 * (24; 52).
Then we carry out the last calculation and find the coordinates of the point D: D (x; y) = (12; 26). That is, D (12; 26).
Answer: C (14; 34) and D (12; 26).