Final answer:
To find the midpoint of the line joining P(6,k) and Q(1-3k,3), we need to find the average of the x-coordinates and the average of the y-coordinates of the two points. We can do this by applying the midpoint formula and solving for the variable k using the given slope of the line. Once we have the value of k, we can substitute it back into the midpoint formula to find the coordinates of the midpoint.
Step-by-step explanation:
To find the midpoint of the line joining P(6,k) and Q(1-3k,3), we need to find the average of the x-coordinates and the average of the y-coordinates of the two points. The x-coordinate of the midpoint is (6 + (1-3k))/2, and the y-coordinate of the midpoint is (k + 3)/2. To find k, we can use the fact that the slope of the line is 1/2. The slope formula is (y2 - y1)/(x2 - x1), so we can substitute the coordinates of P and Q into this formula and solve for k. Once we have the value of k, we can substitute it back into the x-coordinate and y-coordinate formulas to find the coordinates of the midpoint.