Known points A (-2; 5), B (4; 17) – the ends of the segment AB, on this segment there is a point C

| September 30, 2021 | education

Known points A (-2; 5), B (4; 17) – the ends of the segment AB, on this segment there is a point C, the distance of which from A is twice the distance from B. Determine the coordinates of point C.

If it is known that the distance between points C and A is twice the distance between points C and B, we find separately what each coordinate is equal to.

Because the length of the segment along the abscissa between the coordinates of points A and B is equal to

4 – (-2) = 6,

then 2/3 of this segment is equal to 6/3 * 2 = 4.

Find the x coordinate of point C:

(-2) + 4 = 2, i.e. coordinate x = 2.

Because the length of the segment along the ordinate between the coordinates of points A and B is equal to

17 – 5 = 12,

then 2/3 of this segment is equal to 12/3 * 2 = 8.

Find the coordinate at point C:

5 + 8 = 13, i.e. coordinate y = 13.

Answer: point C (2; 13).



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