Question

If A(2,5) B(6,-1) C(-4,-3) are vertices of ∆ABC, find equation of i) median through A ii) Altitude through B​

Answer 1

Answer:

1)8x+y = 12

2) x-3y +6 =0

Step-by-step explanation:

• Given A(2,-4) B(3,3) and C(-1,5) are the vertices of the triangle ABC,

1)Midpoint of 2 points (x₁,y₁) and(x₂,y₂) is given by (x₁+x₂/2,y₁+y₂/2).

• So, Midpoint of BC is (1, 4)

• Median is line joining vertex to the midpoint of the opposite side.

• Hence, median of the triangle through A is the line joining A and the midpoint of BC,

• Thus,Equation of median is line joining (2,-4) and (1,4)

= y+4/x-2 = 8/-1

=>y+4/x-2 = -8

=>y+4 = -8x + 16

=>8x + y = 12 ....Ans

2)Altitude of the triangle through B is line passing through B and perpndicular to AC,

• Now slope of line joining 2 points (x₁,y₁) and(x₂,y₂) is given by y₂-y₁/x₂-x₁.

• Slope of AC will be 9/-3 = -3

• Also if 2 lines with slopes m₁ and slope m₂ are  perpendicular, we have m₁m₂ = -1, Since slope of AC is -3

• We have slope of the altitude through B as -1/-3 = 1/3.So we need to find the equation of line passing through B(3, 3) and having slope 1/3

= y-3/x-3 = 1/3

=>3y -9 = x-3

=>x-3y +6 =0 is the required altitude.