Question

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?

Answer 1

Answer:

$(x_2,y_2)=(9,3)$

Step-by-step explanation:

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

The best approach is to use the section formula which relates to the internal division of a line.

Given a line from $(x_1,y_1) \: to\: (x_2,y_2)$ which is divided in the ratio m:n, the coordinates of the point P of division is derived using the formula:

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

In our given case,

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

m:n=1:3

$(x_1,y_1) =(1,-1)$

Our goal is to determine the end of the stencil $(x_2,y_2)$

Thus:

$(3,0)=\left(\dfrac{1x_2+3(1)}{3+1} ,\dfrac{1y_2+3(-1)}{3+1}\right)\\Matching \: coordinates\\\dfrac{1x_2+3(1)}{3+1}=3\\x_2+3=3*4\\x_2=12-3=9\\\dfrac{1y_2+3(-1)}{3+1}=0\\y_2-3=0*4\\y_2=3+0=3$

Therefore, the end of the stencil is located at, $(x_2,y_2)=(9,3)$

Answer 2

Answer: (1.25,-0.75)

Step-by-step explanation:

ratio 1:3, we can  say as a fraction its 1/4

look at the x coordinates

(1,-1) (3,0)

its a distance of 2

1/4 * 2= 1/4

look at the y coordinates

(1,-1) (3,0)

its a distance of 1

1/4 * 1 = 1/4

so substitute these numbers in one of the coordinates

In this case im going to use (1,-1)

1 + 1/4 = 5/4 or 1.25

-1 + 1/4 = -3/4 = -0.75

Hope this helped in some way