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NEED HELP GEOMETRY

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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?

Feb 19, 2018

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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

Feb 19, 2018