Point C divides the segment AB in a ratio of 3: 5 (from A to B). The ends of the segment are points

Point C divides the segment AB in a ratio of 3: 5 (from A to B). The ends of the segment are points A (2; 3), B (10; 11). Find point C.

The ratio 3: 5 means that the segment AB consists of 3 + 5 = 8 equal parts. The coordinates of the points A (2; 3) and B (10; 11) – indicate that the segment under consideration lies in the first coordinate quarter. The projection from B onto the Y-axis to the point of intersection with a ray from A, drawn parallel to the same Y, is the leg of a right-angled triangle. The second leg is a section of the beam from A to the same intersection point.

Let’s determine the size of these legs:

11 – 3 = 8;

10 – 2 = 8.

We see that the triangle is isosceles with an apex of 90º. The dimensions of these legs are exactly according to the number of parts of the ratio, which gives us the right to determine the coordinates of C as follows:

2 + 3 = 5 (x coordinate);

3 + 3 = 6 (y).

That is, C (5; 6).

This point can be found by subtracting 5 from the coordinates B:

10 – 5 = 5 (x);

11 – 5 = 6 (y).

The same result C (5; 6).

You can finally be convinced of the correctness of the answer by constructing.