+642
8) What are the coordinates of the midpoint of the line segment with endpoints D(-5, 3) E(2, -2)?
9) Point A is located at (3, 2 ) and point B is located at ( 10, 12). What are the coordinates of the point that partitions the directed line segment in a 3: 2 ratio?
10) Point A is located at (1, 2) and point B is located at ( 13, 8). What are the coordinates of the point that partitions the directed line segment in a 5: 1 ratio?
+9481 8)
We can think of this as the point that divides the line segment in a 1:1 ratio.
x-coordinate = -5 + 1/(1 + 1) * (2 - -5) = -5 + 1/2 * 7 = -5 + 7/2 = -1.5
y-coordinate = 3 - 1/(1 + 1) * (3 - -2) = 3 - 1/2 * 5 = 3 - 5/2 = 0.5
The coordinates are (-1.5, 5.5)
Here's a graph: https://www.desmos.com/calculator/m4soc58v9b
9)
x-coordinate = 3 + 3/(3 + 2) * (10 - 3) = 3 + 3/5 * 7 = 3 + 21/5 = 7.2
y-coordinate = 2 + 3/(3 + 2) * (12 - 2) = 2 + 3/5 * 10 = 2 + 30/5 = 8
The coordinates are (7.2, 8)
Here's a graph: https://www.desmos.com/calculator/sravdf6fly
I changed the step size and shifted all the points to the left so that you can see that (7.2, 8) is three-fifths from point A in the x and y direction.
10)
x-coordinate = 1 + 5/(5 + 1) * (13 - 1) = 1 + 5/6 * 12 = 1 + 60/6 = 11
y-coordinate = 2 + 5/(5 + 1) * ( 8 - 2 ) = 2 + 5/6 * 6 = 2 + 5 = 7
The coordinates are (11, 7)
Here's a graph: https://www.desmos.com/calculator/goetjvhgit
