Question

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) By the way if this helps, the 3rd option is wrong

Answer 1

Answer:

(8,-1)

Step-by-step explanation:

A line segment AB with points A at ($x_1,y_1$) and B is at ($x_2,y_2$). If there is a point O that divides the line in ratio a:b, the coordinates of O(x, y) is given as:

$x=\frac{a}{a+b}(x_2-x_1)+x_1,y= \frac{a}{a+b}(y_2-y_1)+y_1$.

Given that point (2,1) divides the segment with endpoints (-1, 2) and (x, y) in a 1:2 ratio. The coordinates of x and y of the end of the stencil are:

$2=\frac{1}{2+1}(x-(-1))+(-1)\\\\2=\frac{1}{3}(x+1)-1\\\\2+1=\frac{1}{3}(x+1)\\\\x+1=9\\\\x=9-1\\\\x=8$

$1=\frac{1}{2+1}(y-2)+2\\\\1=\frac{1}{3}(y-2)+2\\\\1-2=\frac{1}{3}(y-2)\\\\y-2=-3\\\\y=-3+2\\\\y=-1$

The end of the stencil is located at (8, -1)