The midpoint is exactly in the midle of line segment PR.
This applies fro both the x and y coordinates. The method you have to apply is as follows:
y-coordinate:
1) Calculate the distance of P and R over the y-axis:
dPR = yR - yP = 15 - 3 = 12
2) Divide the calculated distance by 2, that way you'll be calculating the distance between the endpoints and the midpoint.
dyM = 12/2 = 6
3) Now you can calculate the value fo the y-coordinate of the midpoint by adding it to the y-coordinate of the lower endpoint P or subtracting it from the upper endpoint R:
yM= yP + dyM = 3 + 6 = 9
x-cordinate:
1)Calculate the distance of P and R over the x-axis
dPR= xR-xP= 11-1= 10
2) Divide it by two to get the distance to the midpoint:
dxM= 10/2=5
3) Calculate the x-coordinate of the midpoint by adding it to the x-coordinate of P or subtracting it from the x-coordinate of R
xM= xR - dxM= 11-5= 6
The coordinates for the midpoint are M(6,9)
Point Q
To calculate this point you have to follow the same method as before, with exception that the distance between P, Q and R is PQ:QR= 2:3
If you add both rations you'll get a total of 5, using this total as a denominatior you can express the ratio as fractions so that:
PQ:QR= 2:3= 2/5 and 3/5
The distance between P and Q is 2/5 and the distance between Q and R is 3/5. > This means that if you divide the segment line PR in 5, Q will be found two fifths away deom endpoint P and 3 fifths away from endpoint R.
Using either one you can calculate the coordinates for Q. I'll use the distance PQ=2/5
Calculate the measure of the line segment PQ by multiplying the distance PR by 2/5:
dPQ= dPR*2/5= 12*2/5= 4.8
y- coordinate:
yQ= yP + dPQ= 3+4.8=7.8
x-coordinate:
xQ= xP + dPQ= 1+4.8= 5.8
The coordinates for point Q (5.8,7.8)