Question

Find the vertices of a triangle , if the mid points the sides are ( 12, 12), ( 8, 4), ( 10, 5).

Answer 1

Step-by-step explanation:

ANSWER

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)