The segment with the ends A (2; 3) and B (10; 11) is divided by point C in the ratio

| April 25, 2021 | education

The segment with the ends A (2; 3) and B (10; 11) is divided by point C in the ratio 3: 5 (from A to B). Find the sum of the coordinates of point C.

1. Let’s write down the formula for finding the “X” coordinate of point C:

Xc = (Xa + λ * Xb) / (1 + λ), where Xa and Xb are the “X” coordinates of points A and B, and λ is the ratio of the segments AC and CB, that is, 3: 5.

Find Xc:

Xc = (2 + 3/5 * 10) / (1 + 3/5) = (2 + 6) / (8/5) = 8 * 5/8 = 5.

2. Formula for finding the “Y” coordinate of point C:

Yс = (Yа + λ * Yb) / (1 + λ), where Yа and Yb – coordinates “Y” of points A and B

Yс = (3 + 3/5 * 11) / (1 + 3/5) = (3 + 33/5) / (8/5) = (48/5) / (8/5) = 48/5 * 5/8 = 6.

3. Find the sum of the coordinates of point C:

Xc + Yc = 5 + 6 = 11.

Answer: the sum of the coordinates of point C 11.



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