Question

If the points (10,5) , (8,4) , and (6,6), are the mid points of the sides of the triangle, Find its vertices. Ans : (4,5 ) , (8,7),(12,3)

Answer 1

given,
A(a,b) B(c,d) C(e,f)
Midpoint of AB:
(10,5)=(a+c/2),(b+d/2)
=>a+c=20...........(1) and b+d=10............(2)
Midpoint of BC:
(8,4)=(c+e/2),(d+f/2)
=>c+e=16............(3) and d+f=8..............(4)
Midpoint of AC:
(6,6)=(a+e/2),(b+f/2)
=>a+e=12...........(5) and b+f=12...............(6)
(1)-(3)=>
=>a+c-c-e=20-16
=>a-e=4...........(7)
(5)+(7)=>
=>a+e+a-e=12+4
=>2a=16=> a=8
substitute a=8 in (1)
=>8+c=20
=>c=12
substitute c=12 in (3)
=>12+e=16
=>e=4
(2)-(4)=>
=> b+d-d-f=10-8
=>b-f=2................(8)
(8)+(6)=>
=>b-f+b+f=2+12
=>2b=14
=>b=7
substitute b=7 in (2)
=>7+d=10
=>d=3
substitute d=3 in(4)
=>3+f=8
=>f=5
A(8,7) B(12,3) C(4,5)

HOPE IT IS USEFUL

Answer 2

Answer:

Step-by-step explanation:

A(a,b) B(c,d) C(e,f)

Midpoint of AB:

(10,5)=(a+c/2),(b+d/2)

=>a+c=20........(1) and b+d=10.........(2)

Midpoint of BC:

(8,4)=(c+e/2),(d+f/2)

=>c+e=16.......(3) and d+f=8............(4)

Midpoint of AC:

(6,6)=(a+e/2),(b+f/2)

=>a+e=12......(5) and

b+f=12..........(6)

(1)-(3)=>

=>a+c-c-e=20-16

=>a-e=4.......(7)

(5)+(7)=>

=>a+e+a-e=12+4

=>2a=16=> a=8

substitute a=8 in (1)

=>8+c=20

=>c=12

substitute c=12 in (3)

=>12+e=16

=>e=4

(2)-(4)=>

=> b+d-d-f=10-8

=>b-f=2.........(8)

(8)+(6)=>

=>b-f+b+f=2+12

=>2b=14

=>b=7

substitute b=7 in (2)

=>7+d=10

=>d=3

substitute d=3 in(4)

=>3+f=8