Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (2,

Question

3 months ago

12

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)

Mathematics

2 answers:

PIT_PIT [12.4K] · Answer 1 · 2026-03-04T18:16:54+03:00

Answer:

(A)(12, 9)

Step-by-step explanation:

Provided:

The starting point of the stencil's left edge is at (2, -1).

A designated point, referred to as Q on the stencil, is located at (4, 1).

Point Q divides the stencil in a 1:4 ratio.

We are tasked with determining the endpoint of the stencil.

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

For calculating the internal division of a line segment with initial point $(x_1,y_1)$ and end point $(x_2,y_2)$ in the ratio m:n, we apply 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

Consequently:

$(4,1)=(\dfrac{1x_2+4*2}{1+4},\dfrac{1y_2+4*-1}{1+4} )\\(4,1)=(\dfrac{x_2+8}{5},\dfrac{y_2-4}{5} )\\$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 selected choice is A.

Zina [12.3K] · Answer 2 · 2026-03-04T18:16:27+03:00

Zina [12.3K]3 months ago

4 0

Answer:

(A)(12, 9)

Step-by-step explanation:

I took the examination and answered this question correctly.