Question

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?
(12, 9)
(10, 7)
(3.5, 0.5)
(2.5, −0.5)

Answer 1

Answer:

(A)(12, 9)

Step-by-step explanation:

Given:

The beginning of the left edge of the stencil falls at (2, −1).

A point, say Q on the stencil is at  (4, 1).

Point Q divides the stencil into the ratio 1:4.

We are required to find the end of the stencil.

Mathematically, Point Q divides the stencil internally in the ratio 1:4.

For internal division of a line with beginning point $(x_1,y_1)$ and end point $(x_2,y_2)$ in the ratio m:n, we use the formula

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

$(x_1,y_1)=(2, -1)$, $(x_2,y_2)=?$, Q(x,y)=(4,1), m:n=1:4

Therefore:

$(4,1)=(\dfrac{1x_2+4*2}{1+4} ,\dfrac{1y_2+4*-1}{1+4} )\\(4,1)=(\dfrac{x_2+8}{5} ,\dfrac{y_2-4}{5} )\\ Therefore:\\\dfrac{x_2+8}{5}=4\\x_2+8=4X5\\x_2=20-8=12\\ Similarly\\\dfrac{y_2-4}{5}=1\\y_2-4=5\\y_2=4+5=9\\(x_2,y_2)=(12,9)$

The correct option is A.

Answer 2

Answer:

(A)(12, 9)

Step-by-step explanation:

I took the test and got his question correct.