Final answer:
The equation of the median OM is y = (3/5)x + 6/5, and the equation of the altitude OD is x = 0.
Step-by-step explanation:
Equation of Median OM:
Given the points A(0,6) and B(10,0), the coordinates of the midpoint M of segment AB can be found by taking the average of the x-coordinates and the average of the y-coordinates. So, the coordinates of M are ((0+10)/2, (6+0)/2) = (5,3). The slope of the line OM can be found using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are the coordinates of M and the origin O respectively. Plugging in the values, we get (3-0)/(5-0) = 3/5. Finally, we can use the point-slope form of a line, which states that y-y1=m(x-x1), where m is the slope and (x1,y1) are the coordinates of a point on the line. Substituting the values, we get y-3=(3/5)(x-5), which simplifies to y = (3/5)x + 6/5.
Equation of Altitude OD:
Since O is the origin, the coordinates of O are (0,0). The equation of a vertical line passing through O is x=0, which means the equation of the altitude OD is x=0.