Question

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.

Answer 1

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

Explanation:

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

`AB^(2)` =
`AC^(2)` +
`BC^(2)`

=
`10^(2)` +
`6^(2)`

= 100 + 36

= 136

AB =
`√(136)`

AB = 11.6619

AB = 11.66

≅ 11.7 units

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

AQ =
`(2)/(5)` × AB

=
`(2)/(5)` × 11.66

= 4.664

AQ = 4.664

AQ ≅ 4.7 units

QB =
`(3)/(5)` × AB

=
`(3)/(5)` × 11.66

= 6.996

QB ≅ 7.0 units

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