The point which divides the line segment joining the points (7, –6) and (3, 4) inratio 1 : 2 internally lies in the

The formula to find the point that divides a line segment into a given ratio is given by:

((m1x2 + m2x1) / (m1 + m2), (m1y2 + m2y1) / (m1 + m2))

where (x1, y1) and (x2, y2) are the coordinates of the two points and m1 : m2 is the given ratio.

Here, (x1, y1) = (7, -6) and (x2, y2) = (3, 4). The given ratio is 1 : 2, so m1 = 1 and m2 = 2.

Substituting these values into the formula, we get:

((13 + 27) / (1 + 2), (14 + 2(-6)) / (1 + 2))

Solving this, we get:

((3 + 14) / 3, (4 - 12) / 3)

So, the point that divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1 : 2 internally is (17/3, -8/3).