Final answer:
The y-coordinate of point E is 0.
Step-by-step explanation:
To find the y-coordinate of point E, we need to use the fact that overline ED is parallel to overline AC. Since the x-coordinate of point E is given as 12, we can use the slope of overline AC to find the y-coordinate of point E. Let's assume the y-coordinate of point E is y. The slope of overline AC is (y2 - y1) / (x2 - x1), where (x1, y1) is a point on overline AC and (x2, y2) is point E.
Since overline AC is parallel to overline ED, the slope of overline AC and overline ED will be the same. So, we can set up the equation: (y - 12) / (x - 0) = (y2 - y1) / (x2 - x1). Now, we can substitute the known values: (y - 12) / (12 - 0) = (y - 0) / (x - 12). Cross multiplying, we get: (y - 12) * (x - 12) = y * (12 - 0). Expanding the equation, we get: yx - 12y - 12x + 144 = 12y. Simplifying, we get: yx - 12y - 12x + 144 = 12y.
Combining like terms, we get: yx - 24y - 12x + 144 = 0. Rearranging the equation, we get: yx - 36y - 12x + 144 = 0. This is the equation of a line. To find the value of y, we can use the x-coordinate of point E, which is 12. Substituting x = 12 into the equation, we get: y * 12 - 36y - 12 * 12 + 144 = 0. Simplifying, we get: 12y - 36y - 144 + 144 = 0. Combining like terms, we get: -24y = 0. Solving for y, we get: y = 0 / -24. Therefore, the y-coordinate of point E is 0.