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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)

Sagot :

MrRoyal

Answer:

(9,3)

Step-by-step explanation:

Represent the beginning with B

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

Represent the alignment point with C

[tex]C(x,y) = (3,0)[/tex]

At C, we have:

[tex]m:n = 1:3[/tex]

Required

Determine the end of the stencil

To do this, we make use of the following line partition formula;

[tex]C(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2+ ny_1}{m+n})[/tex]

Substitute values

[tex](3,0) = (\frac{1*x_2 + 3*1}{1+3},\frac{1*y_2+ 3*-1}{1+3})[/tex]

[tex](3,0) = (\frac{x_2 + 3}{4},\frac{y_2- 3}{4})[/tex]

Multiply through by 4

[tex]4*(3,0) = (\frac{x_2 + 3}{4},\frac{y_2- 3}{4})*4[/tex]

[tex](12,0) = (x_2 + 3,y_2- 3)[/tex]

By comparison:

[tex]x_2 +3 = 12\\[/tex]

[tex]x_2= 9[/tex]

and

[tex]y_2 - 3 = 0[/tex]

[tex]y_2 = 3[/tex]

So, the coordinates are: (9,3)

Answer:the person above me is correct it is (9,3)

Step-by-step explanation:

I took the test and this was my answer

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