Home
Class 12
MATHS
In a DeltaABC, A = (2,3) and medians thr...

In a `DeltaABC, A = (2,3)` and medians through B and C have equations `x +y - 1 = 0` and `2y - 1 = 0`
Equation of side BC is (a) `5x +13y +11 = 0` (b) `5x - 3y = 1` (c) `5x = 3y` (d) `5x +13y - 11 = 0`

A

`5x +13y +11 = 0`

B

`5x - 3y = 1`

C

`5x = 3y`

D

`5x +13y - 11 = 0`

Text Solution

Verified by Experts

The correct Answer is:
A

Centroid is the point of intersection of `x +y -1 = 0, 2y -1 = 0` or `D ((1)/(2),(1)/(2))`
Slope of AD is `(3-(1)/(2))/(2-(1)/(2)) =(5)/(3)`
`:.` Equation of AD is `y - 3 = (5)/(3) (x-2)` or `5x - 3y - 1 = 0`
A point of `CF: 2y - 1 = 0` is `(alpha, (1)/(2))`
Let this be the midpoint of AB.
`:.` B is `(2alpha -2,-2)` which lies on median `BE: x +y - 1 = 0`
`:. 2alpha -2-2-1 = 0 :. alpha =(5)/(2)`
`:. B (3,-2)`
G divides CF in 2:1
`:. C = ((-7)/(2),(1)/(2))`
`:.` Equation of BC is `(y+2)/((1)/(2)+2) = (x-3)/((-7)/(2)-3)`
or `(y+2)/(5) =(x-3)/(-13)`
or `5x +13y +11 = 0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|32 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • STATISTICS

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

Similar Questions

Explore conceptually related problems

In a DeltaABC, A = (2,3) and medians through B and C have equations x +y - 1 = 0 and 2y - 1 = 0 Equation of median through A is

Find the distance between the lines 5x -12y + 2 = 0 and -5x + 12y + 3 = 0

If x = 2k + 1 and y = k is a solutions of the equation 5x + 3y - 7 = 0, find the value of k.

Express each of the following equations in the form of ax + by + c = 0 and write the values of a, b and c. (i) 3x + 4y = 5 (ii) x - 5 = sqrt3y (iii) 3x = y (iv) x/2+y/2=1/6 (v) 3x - 7 = 0

If x-2y+4=0a n d2x+y-5=0 are the sides of an isosceles triangle having area 10s qdotu n i t s , the equation of the third side is (a) 3x-y=-9 (b) 3x-y+11=0 (c) x-3y=19 (d) 3x-y+15=0

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

The equation of the plane through the intersection of the planes x+2y+3z-4=0 and 4x+3y+2z+1=0 and passing through the origin is (a) 17x+14y+11z=0 (b) 7x+4y+z=0 (c) x+14+11z=0 (d) 17x+y+z=0

In a triangle A B C , if A is (2,-1),a n d7x-10 y+1=0 and 3x-2y+5=0 are the equations of an altitude and an angle bisector, respectively, drawn from B , then the equation of B C is (a) a+y+1=0 (b) 5x+y+17=0 (c) 4x+9y+30=0 (d) x-5y-7=0

If (0, a) and (b, 0) are the solutions of the following linear equations. Find ‘a’ and ‘b’. (i)8x - y = 34 (ii) 3x = 7y - 21 (iii)5x - 2y + 3 = 0

The equation of a straight line passing through the point (2, 3) and inclined at an angle of tan^(-1)(1/2) with the line y+2x=5 , so the equation of the line is/ are: (a) y=3 (b) x=2 3x+4y-18=0 (d) 4x+3y-17=0