Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (−1, 2). She wants to align an important detail on the left edge of her stencil at (2, 1). She knows this is 1:2 of the way to where she wants the end of the stencil. Where is the end of the stencil located?

(0, 5)
(8, −1)
(0.5, 1.5)
(1, 1.7)

The correct option is: (0.5, 1.5)

Step-by-step explanation:

I will use the notation (x, y) to solve this.

The start is at (-1, 2)

And the point (2,1) is at 1:2 of the point where she wants to finish the stencil. (so the actual end of the stencil is at half the distance between these two points)

First, we calculate the distance between these two points.

Now, we assume that the line is a straigth line, se we can suppose that there is a linear equation for this line, we can get the slope of it as:

s = (y2 - y1)/(x2 -x1)

in this case

s = (1 - 2)/(2 - (-1)) = -1/3

The slope os s = -1/3

then our line is:

y(x) = -1/3*x + b

and we know that when x = -1, we have:

y(-1) = 2 = -1/3*-1 + b = 1/3 + b

b = 2 - 1/3 = 5/3.

y(x) = -1/3*x + 5/3

then, knowing that this is a linear relation, then if we want the half point between the two given ones, we need to valuate our linear relationship in the middle of the two x values that we have.

x = -1 and x = 2.

To calculate the middle value, we calculate the difference between these numbers and we divide it by 2, and then we add that number to the smaller (in this case -1)

x0 = -1 + (2 - (-1))/2  = -1 + 1.5 = 0.5

Now we evaluate our linear equattion in this point:

y(0.5) =  -1/3*0.5+ 5/3 = 1.5

The correct option is: (0.5, 1.5)

(8, -1)

Step-by-step explanation:

If your on question 3 of (04.03 MC) that should be the answer.