Question

What are the coordinates of the point 3/5 of the way from A(-4,-4) to B(6,6)

Answer 1

The coordinates of the point 3/5 of the way from A(-4,-4) to B(6,6) are (2, 2).

Explanation:

Given the points

• A(-4,-4)

• B(6,6)

We need to find the coordinates of the point 3/5 of the way from A(-4,-4) to B(6,6).

Let P be the required point, then

AP : AB = 3 : 5

as

• AB = AP + BP

so

AP / AB = 3/5

AP / (AP + BP) = 3/5

5AP = 3(AP + BP)

5AP = 3AP + 3BP

2AP = 3BP

AP/BP = 3/2

AP : BP = 3 : 2

The formula of the coordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n is:

`\left((mc+na)/(m+n),\:(md+nb)/(m+n)\right)`

For the given division,

m : n = 3 : 2

Thus, the coordinates of the point P are:

`\left((3\left(6\right)+2\left(-4\right))/(3+2),\:(3\left(6\right)+2\left(-4\right))/(3+2)\right)`

`=\left((18-8)/(5),\:(18-8)/(5)\right)`

`=\left((10)/(5),\:(10)/(5)\right)`

`=\left(2,\:2\right)`

Therefore, the coordinates of the point 3/5 of the way from A(-4,-4) to B(6,6) are (2, 2).