SOLUTION: Find the perimeter of the triangle whose vertices are p(6,4) Q(-3,1) and R(9,-5)

Algebra ->  Coordinate-system -> SOLUTION: Find the perimeter of the triangle whose vertices are p(6,4) Q(-3,1) and R(9,-5)      Log On


   

Question 928179: Find the perimeter of the triangle whose vertices are p(6,4) Q(-3,1) and R(9,-5)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
p(6,4) Q(-3,1) and R(9,-5)
first draw a triangle:


to find perimeter, we need the length of sides, and the length of side is equal to distance between two points
so, we will find the distance between points p(6,4) and Q(-3,1), then Q(-3,1) and R(9,-5), and finally p(6,4) and R(9,-5)

a) the distance between points p(6,4) and Q(-3,1)

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%286--3%29%5E2+%2B+%284-1%29%5E2%29=+9.48683298050514+


For more on this concept, refer to Distance formula.


so, the length of the side pQ=9.5

b) the distance between points Q(-3,1) and R(9,-5)
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%289--3%29%5E2+%2B+%28-5-1%29%5E2%29=+13.4164078649987+


For more on this concept, refer to Distance formula.



the length of the side QR=13.4

c) the distance between points p(6,4) and R(9,-5)
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%289-6%29%5E2+%2B+%28-5-4%29%5E2%29=+9.48683298050514+


For more on this concept, refer to Distance formula.



the length of the side pR=9.5

then, perimeter P=pQ%2BQR%2BpR=>P=9.5%2B13.4%2B9.5=>P=32.4