Respuesta :

Given the points

A(x₁,y₁) = (4,0)

B(x₂,y₂) = (6,8)

ratio l:m = 1:2

The formula that we use to find the point P that divides the given line segment in the ratio l:m is

P(x,y) = [tex](\frac{lx2+mx1}{l+m} ,\frac{ly2+my1}{l+m} )[/tex]

=[tex](\frac{1.6+2.4}{1+2} , \frac{1.8+2.0}{1+2} )[/tex]

=[tex](\frac{6+8}{3} ,\frac{8+0}{3} )[/tex]

=[tex](\frac{14}{3}, \frac{8}{3} )[/tex]

Hence the right option is B)

carlosego

Answer:

Then point P is ([tex]\frac{14}{3}, \frac{8}{3}[/tex])


The correct answer is option 2.

Step-by-step explanation:

First let's calculate the distance between points A and B


A: (4.0)


B: (6.8)



The distance in x between both is:


[tex]X_2-X_1 = 6-8 = 2[/tex]

The distance in the y axis between both is:


[tex]y_2-y_1 = 8-0 = 8[/tex].


We know that the point divides the line segment in a 1: 2 ratio as shown in the following diagram



A --------- P ------------------- B


Where the distance PB is twice as large as the AP distance.



Then [tex]AP = \frac{1}{3}AB\\\\PB = \frac{2}{3}AB.[/tex]


Therefore Point P is at a distance d = 1/3 * ([tex]X_{2}-X_{1}[/tex]) from point A.


So:



[tex]P_{x} = 4 + \frac{1}{3}2 = \frac{14}{3}\\\\P_{y} = 0 + \frac{1}{3}8 = \frac{8}{3}[/tex]



Then point P is ([tex]\frac{14}{3}, \frac{8}{3}[/tex])


The correct answer is option 2.