Cho A(1;6), B(2;-6), C(-1;1) a.C/m ABC lập thành 1 tam giác b.Tìm trọng tâm G, trực tâm H c.Tính chiều cao AA' của 🔺️ABC, diện tích 🔺️ABC?

By Trang Ánh Nam -

Cho A(1;6), B(2;-6), C(-1;1)

a.C/m ABC lập thành 1 tam giác

b.Tìm trọng tâm G, trực tâm H

c.Tính chiều cao AA' của 🔺️ABC, diện tích 🔺️ABC?

Giải:

a.

Ta có:

=(1;-12) ;
=(-2,-5)

Dể thấy hai vecter này không cùng phương nên 3 điểm A,B,C không thẳng hang. Suy ra A,B,C lập thành 1 tam giác.

b. G=(2/3;/3)  (tổng 3 tọa độ 3 điểm trên chia 3)

gọi H(n,h) là trực tam ABC.

=(n-2;h+6)

=(n+1;h-1)

Theo tính chất trục tam ta có:

=>

=>

<=>

<=>

 

H=(-13,0)

c. Gọi A’=(p,q) là điểm cần tìm.

Ta có: =(p-1;q-6), =(-14,-6), =(-3;7), =(p+1;q-1)

Vì AA’ là đường cao của tam giác ABC nên ta có:

 

=>

=>

=>

=>

A’=()

=>=() =>||=

Diện tích tam giác ABC là:

AA’.BC==29

 

 

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