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
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...