Question 12 (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 ( 1 , -1 ). She wants to align an
important detail on the left edge of her stencil at . She knows this is of the way to where she wants the end of the stencil. Where is the end of
the stencil located?
a
b
c
d 9,3

Ask by O'Quinn Higgins. in the United States

Jan 23,2025

Question

Question 12 (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 ( 1 , -1 ). She wants to align an
important detail on the left edge of her stencil at . She knows this is of the way to where she wants the end of the stencil. Where is the end of
the stencil located?
a
b
c
d 9,3

Ask by O'Quinn Higgins. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To determine the location of the end of Annie's stencil, let's break down the information:

1. **Starting Point:** $$(1, -1)$$
2. **Important Detail Point:** $$(3, 0)$$
3. **Ratio:** The point $$(3, 0)$$ is $$1:3$$ of the way to the end.

This ratio implies that from the starting point to $$(3, 0)$$ is 1 part, and from $$(3, 0)$$ to the end is 3 parts, making a total of 4 parts.

Let's denote the end of the stencil as $$(x, y)$$.

Using the ratio, we can set up the following equations based on the coordinates:

$$
\begin{cases}
3 = 1 + \frac{1}{4}(x - 1) \
0 = -1 + \frac{1}{4}(y + 1)
\end{cases}
$$

**Solving for $$x$$:**
$$
3 - 1 = \frac{1}{4}(x - 1) \
2 = \frac{1}{4}(x - 1) \
x - 1 = 8 \
x = 9
$$

**Solving for $$y$$:**
$$
0 + 1 = \frac{1}{4}(y + 1) \
1 = \frac{1}{4}(y + 1) \
y + 1 = 4 \
y = 3
$$

So, the end of the stencil is located at $$(9, 3)$$.

**Answer:**  
**d** $$ (9,\ 3) $$
The end of the stencil is at $$(9, 3)$$.