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

Answer:

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)

Step-by-step 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

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

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:

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$x=\frac{\left(3\right)\left(1\right)+\left(13\right)\left(4\right)}{4+1}$

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

$x=\frac{3\cdot \:1+13\cdot \:4}{4+1}$

$x=\frac{55}{4+1}$         ∵ $3\cdot \:1+13\cdot \:4=55$

$x=\frac{55}{5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{55}{5}=11$

$x=11$

Finding y-coordinate:

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{\left(-5\right)\left(1\right)+\left(-15\right)\left(4\right)}{4+1}$

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

$y=\frac{-5\cdot \:\:1-15\cdot \:\:4}{4+1}$

  $=\frac{-65}{4+1}$            ∵ $-5\cdot \:1-15\cdot \:4=-65$

  $=\frac{-65}{5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$y=-\frac{65}{5}$

$y=-13$

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)