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 \( (3,0) \). She knows this is \( 1: 3 \) of the way to where she wants the end of the stencil. Where is the end of the stencil located? a \( \quad(1.5,-0.75) \) b \( \quad(2.5,-0.25) \) c \( (6,2) \) d 9,3\( ) \)

To determine the location of the end of the stencil, we need to find the total length of the stencil based on the proportional positioning of the important detail. Since the detail at (3, 0) is \( \frac{1}{3} \) of the way to the end of the stencil, we can set up a linear journey: the distance from (1, -1) to (3, 0) is the first \( 1:3 \) proportion of the total distance. Calculating the distance, we find that from (1, -1) to (3, 0) is a vector of (3 - 1, 0 - (-1)) = (2, 1). Given \( (1, -1) + k(2, 1) = (x, y) \) for \( k = 3 \) gives us the end location as: \[ (x,y) = (1 + 6, -1 + 3) = (7, 2) \] However, this point is not on the answer list. Correctly applying the ratio directly would yield the end point: \[ (1, -1) + 3 \cdot (3 - 1, 0 - (-1)) = (7, 2) \] This incorrect string of math led to confusion affecting the ultimate decisions. So, checking the answer choices, after calculation and verification, we would indicate it must have been adjusted here or probably the proportions reinterpreted from original intention fell from reinterpretation behind awareness en route (,3). Let’s conclude with needing proper placement here.