7. Find the equation of the median from B, in ABC whose vertices are A(1,5), B(5,3), and C(-3,-2).

yeah

Step-by-step explanation:

Answer

Median bisects the line.

D≡(

2

−3+5

,

2

−9−8

)≡(1,

2

−17

)

E≡(−

2

1+5

,

2

6−8

)≡(2,−1)

F≡(−

2

1−3

,

2

6−9

)≡(−2,

2

−3

)

∴ equation of AD:(y−y

1

)=(

x

2

−x

1

y

2

−y

1

)

AD

(x−x

1

)

⇒(y−6)=

⎝

⎜

⎜

⎛

1+1

2

−17

−6

⎠

⎟

⎟

⎞

(x+1)⇒(y−6)=−

4

29

(x+1)

⇒

4

29

x+y−6+

4

29

=0

AD⇒29x+4y+5=0

equation of BE:(y+9)=(−

2+3

1+9

)

BE

(x+3)

⇒(y+9)=

5

8

(x+3)⇒5y+45=8x+24

BE⇒8x−5y−21=0

Equation of CF:(y+8)=

⎝

⎜

⎜

⎛

−2−5

−

2

3

+8

⎠

⎟

⎟

⎞

CF

(x−5)

⇒(y+8)=−

14

13

(x−5)⇒14y+112=−13x+65

CF:13x+14y+47=0