Question

locate the point on the line segment A (3,-5) and B (13,-15) given that the point is 4/5 of the way from A to B. Show your work

Answer 1

The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

Explanation:

As the line segment has the points:

• A(3, -5)

• B(13, -15)

Let (x, y) be the point located on the line segment which is 4/5 of the way from A to B.

Using the formula

`x=(x_(1)m_(2)+x_(2)m_(1))/(m_(1)+m_(2))`

`y=(y_(1)m_(2)+y_(2)m_(1))/(m_(1)+m_(2))`

Here, the point (x , y) divides the line segment having end points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ from the point (x₁, y₁).

As (x, y) be the point located on the line segment which is 4/5 of the way from A to B, meaning the distance from
`A` to
`(x , y)` is
`4` units, and the

distance from
`(x , y)` to B is 1 unit, as
`5 - 4 = 1`.

Thus

m : n = 4 : 1

so

Finding x-coordinate:

`x=(x_(1)m_(2)+x_(2)m_(1))/(m_(1)+m_(2))`

`x=(\left(3\right)\left(1\right)+\left(13\right)\left(4\right))/(4+1)`

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a`

`x=(3\cdot \:1+13\cdot \:4)/(4+1)`

`x=(55)/(4+1)` ∵
`3\cdot \:1+13\cdot \:4=55`

`x=(55)/(5)`

`\mathrm{Divide\:the\:numbers:}\:(55)/(5)=11`

`x=11`

Finding y-coordinate:

`y=(y_(1)m_(2)+y_(2)m_(1))/(m_(1)+m_(2))`

`y=(\left(-5\right)\left(1\right)+\left(-15\right)\left(4\right))/(4+1)`

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a`

`y=(-5\cdot \:\:1-15\cdot \:\:4)/(4+1)`

`=(-65)/(4+1)` ∵
`-5\cdot \:1-15\cdot \:4=-65`

`=(-65)/(5)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)`

`y=-(65)/(5)`

`y=-13`

so

• The x-coordinate = 11

• The y-coordinate = -13

Therefore, the coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)