In the diagram, D and E are the midpoints of AB and BC respectively. Determine the sum of the X and Y coordinates of F, the point of intersection of AE and CD

https://latex.artofproblemsolving.com/5/5/0/55002ffdc5d288b4984c4eba461a467dcced7760.png

Guest Aug 21, 2020

#1**+2 **

First, lets find the coordinates of D and E.

D is the midpoint of A(0,6) and B(0,0)

E is the midpoint of B(0,0) and C(8,0)

The coordinates of D and E are (0,3) and (4,0), respectively.

Since we know the coords of D and E, we can now find the equation for lines AE and CD.

Line AE is a line that passes through the points (0,6) and (4,0).

The slope of AE is (0-6)/(4-0) = -6/4 = -3/2

So AE is a line that has a slope of -3/2 passing through the points (0,6) and (4,0)

y = (-3/2)x + b

6 = 0 + b,

b = 6

**y = (-3/2)x + 6**

Do the same process of finding the slope for line CD and plugging in coords to get the equation for line CD:

**y = (-3/8)x + 3**

Since F is the intersection between the two lines, all we have to do is put the two equations equal to each other and solve.

(-3/2)x + 6 = (-3/8)x + 3

**x = 8/3**

Plug that x value into any y to get

**y = 2**

And from there just add 2 and 8/3 to get:

**14/3 or 4.66...**

KnockOut Aug 21, 2020