Where is the blue dot on the number line?

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

The following division is being performed using multiplication by the reciprocal find the missing numbers is 5/12 divided by x/3 equals 5/12 times x/10 equals 1/x