Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (2, −1). She wants to align an important detail on the left edge of her stencil at (4, 1). She knows this is 1:4 of the way to where she wants the end of the stencil. Where is the end of the stencil located?

Hey There!! The correct answer to this is: (×2, y2) = (9, 3). 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)(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)P(x,y)=(

m+n

mx

2

​

+nx

1

​

​

,

m+n

my

2

​

+ny

1

​

​

)

In our given case,

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

m:n=1:3

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

1

​

,y

1

​

)=(1,−1)

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

2

​

,y

2

​

)

Thus:

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

Therefore, the end of the stencil is located at, $$(x_2,y_2)=(9,3)$$ Sorry If you May not understanding this Because it all tied together. And the correct answer is (9, 3)

Hope It Helps!~ ♡

ItsNobody~ ☆

what is all that apply?

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.