Find the point, Q, along the directed line segment AB that divides AB into the ratio 2:3. The 2:3 ratio means that the line
should be broken up in to 5 equal sections (2 + 3 = 5). This
means that each of the 5 sections can be represented by the
expression AB/5. Therefore, the point that divides AB into the
ratio 2:3 is the distance (AB/5)(2) from A.

Point Q is at a distance of 4.7 units from A.

Step-by-step explanation:

From the graph, AC = 10 units and BC = 6 units. Applying the Pythagoras theorem,

= +

      = +

      = 100 + 36

     = 136

AB =

AB = 11.6619

AB = 11.66

     ≅ 11.7 units

But point Q divides AB into ratio 2:3. Therefore:

AQ = × AB

     =   × 11.66

     = 4.664

AQ = 4.664

AQ ≅ 4.7 units

QB = × AB

     =   × 11.66

     = 6.996

QB  ≅ 7.0 units

So that point Q is at a distance of 4.7 units from A.

correct answers below: