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points P,Q and R are collinear such PQ:QR =2:3 , point P is located at (1,3) and point R is located at (11,15).

points P,Q and R are collinear such PQ:QR =2:3 , point P is located at (1,3) and point-example-1
User Cmxl
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1 Answer

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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)

User Sahinakkaya
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