Question

Question 4 Multiple Choice Worth 4 points)
(04.03 MC)
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)
O (2.5, -0.5)

Answer 1

Answer: The correct answer is (12, 9)

Step-by-step explanation: I got it right on the exam

Answer 2

The end of the stencil is located at (12,9)

Assume the endpoints of the stencil are A and B.

So, we have the following parameters

• Segment A = (2,-1)
• The coordinates of the segment = (x,y) = (4,1)
• Ratio; m : n = 1 : 4

The end of the stencil is then calculated using the following line ratio formula

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

This gives

$(4,1)=(\frac{1 * x_2 + 4 * 2}{1 + 4},\frac{1 * y_2 - 4 * 1}{1 + 4})$

$(4,1)=(\frac{ x_2 + 8}{5},\frac{y_2 - 4}{5})$

Multiply through by 5

$(20,5)=(x_2 + 8,y_2 - 4)$

By comparison, we have:

$x_2 + 8 = 20$

$y_2 - 4 = 5$

Solve for x and y in the equations

$x_2 =12$

$y_2=9$

Hence, the end of the stencil is located at (12,9)

Read more about line segment ratios at:

https://brainly.com/question/11764811