Question

A(1,-5) , B(2,2) , C(-2,4) are the vertices of triangle ABC. Find the equation of :
1. The median through A
2. The altitude through B and
3.The line through C and parallel to AB

Answer 1

8x + y = 3 is The median through A  , 3y = x + 4  is The altitude through B  and  y = 7x + 18  is The line through C and parallel to AB if A(1,-5) , B(2,2) , C(-2,4) are the vertices of triangle

Step-by-step explanation:

A(1,-5) , B(2,2) , C(-2,4)

Mid point of BC = (2 -2)/2 , (2 + 4)/2

= (0 , 3)

A = (1 , - 5)

Slope = (-5 - 3)/(1 - 0)  = - 8

y = -8x + c

3 = 0 + c

=> y = -8x + 3

=> 8x + y = 3

8x + y = 3 is The median through A

Slope of AC = (4 -(-5))/(-2 - 1) = -3

Slope of . The altitude through B = 1/3

y = x/3 + c

2 = 2/3  + c

=> c = 4/3

y = x/3 + 4/3

=> 3y = x + 4  is The altitude through B

Slope of AB = 7

y = 7x + c

passes through C

=> 4 = -14 + c

=> c = 18

=> y = 7x + 18  is The line through C and parallel to AB

Learn more:

The vertices of a triangle ABC are A(3,8)

https://brainly.in/question/8653437

The vertices of an triangle abc area A(-3,2) B(-1,-4)and C(-5,2).if M ...

https://brainly.in/question/8994561