If midpoint of sides of triangle PQR are (1,2) (0,1) (1,0) then find the coordinates of three vertices of triangle PQR
Answers
Answer:
By midpoint formula
the vertices are P=(1/2,3/2) Q=(1,1) R=(1/2,1/2)
Let us look at the answer:
Step-by-step explanation:
The mid-points of triangle are given as A( 1,2) B(0,1) C(1,0) :
Let the co-ordinates of P (x₁,y₁) Q (x₂, y₂) R (x₃, y₃)
By mid-point formula: (x₁+x₂/2 , y₁+y₂/2) = (1,2) ⇒ x₁+x₂= 2 and y₁+y₂= 4 ...(i)
(x₃+x₂/2 , y₃+y₂/2) = (1,0) ⇒ x₃+x₂= 2 and y₃+y₂= 0 ...(ii)
(x₁+x₃/2 , y₁+y₃/2) = (0,1) ⇒ x₃+x₁= 0 and y₃+y₁= 2 ...(iii)
Adding all the three equations, 2(x₁+x₂+x₃) = 4 and 2(y₁+y₂+y₃) = 6
⇒ (x₁+x₂+x₃) = 2 and (y₁+y₂+y₃)= 3 .... (iv)
subtracting (i) from (iv) we get, x₃= 0 and y₃= -1 ⇒ R ( 0, -1)
subtracting (ii) from (iv) we get, x₁= 0 and y₁= 3 ⇒P (0,3)
subtracting (iii) from (iv) we get, x₂= 2 and y₂= 1 ⇒Q (2,1)
So the co- ordinates of P , Q and R are (0,3) ( 2,1) and ( 0, -1)
