Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (1, −1). She wants to align an important detail on the left edge of her stencil at (3, 0). She knows this is 1:3 of the way to where she wants the end of the stencil. Where is the end of the stencil located?

(1.5, −0.75)
(2.5, −0.25)
(6, 2)
(9, 3)

Respuesta :

Answer:

(9,3)

Step-by-step explanation:

The end of the stencil located when the beginning of the left edge  is provided so it should be (9,3).

Calculation of the end of the stencil located:

The given line should be divided in the ratio 1:3 and the coordinate of the point P where the line is divided is (3,0).

So,

Given a line from [tex](x_1,y_1) \: to\: (x_2,y_2)[/tex] that is divided in the ratio m:n,

Now the coordinates of the point P of division should be derived by the below formula:

[tex]P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Since

P(x,y)=(3,0)

m:n=1:3

[tex](x_1,y_1)[/tex] =(1,-1)

So,

[tex](3,0)=\left(\dfrac{1x_2+3(1)}{3+1} ,\dfrac{1y_2+3(-1)}{3+1}\right)\\\\\dfrac{1x_2+3(1)}{3+1}=3\\x_2+3=3*4\\x_2=12-3=9\\\dfrac{1y_2+3(-1)}{3+1}=0\\y_2-3=0*4\\y_2=3+0=3[/tex]

hence, The end of the stencil located when the beginning of the left edge  is provided so it should be (9,3).

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