Respuesta :

Answer:

The coordinates of B are (1,-5).

Step-by-step explanation:

To find the coordinates of point [tex]B[/tex] we will apply section formula.

Its used to find out if any line segment is of any [tex]m_1: m_2[/tex] ratios.

As the lie segment is joining the points internally we will use section formula for internal points.

Lets say that [tex]B[/tex] is having coordinates [tex](k,l)[/tex] then [tex]k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}[/tex] and [tex]l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}[/tex]

Now we have [tex]A=(8,7)[/tex] we call it [tex](x_1,y_1)[/tex] then [tex]C=(7,-13)[/tex] we call it [tex](x_2,y_2)[/tex].

And [tex]m_1=3[/tex],[tex]m_2=2[/tex]

Plugging all the values in section formula we have.

[tex]k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}[/tex]

[tex]k=\frac{3(7) +2(-8)}{2+3}[/tex]

[tex]= \frac{21-16}{5}= 1[/tex]

Similarly

[tex]l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}[/tex]

[tex]l=\frac{3(-13) +2(7)}{2+3}[/tex]

[tex]l=\frac{-39+14}{5}= -5[/tex]

So the coordinates of [tex]B =(1,-5)[/tex]

The coordinates of B are (-1, -5).

What is section formula?

The Section formula is used to find the coordinates of the point that divides a line segment (externally or internally) into some ratio.

We have,

A(-8,7) and C(7,-13) and AB:BC = 3:2.

let the coordinates of B is (x,y)

Using section formula,

x= [tex]\frac{mx_1+nx_2}{m+n}[/tex] and y= [tex]\frac{my_1+ny_2}{m+n}[/tex]

So,

  x= 3*7+2(-8)/3+2

  x= 21-16/5

  x= -5/5

  x=-1.

y= 3(-13)+2*7/3+2

y= -39+14/5

y= -25/5

y=-5

Hence, the coordinates of B is (-1, -5)

Learn more about section formula here:

https://brainly.com/question/11888968

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