Question

4. In ∆ABC if the equation of sides AB is y-2=0, BC is y = 3x - 7 and AC is 2y + x = 0 , then the coordinates of points A and B are ?​

Answer 1

Answer:

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Step-by-step explanation:

Let co-ordinates of B be (x1,y1) & C be (x2,y2)

∴ (5,6) is the mid point,

so, 2x1+x2=5,2y1+y2=6

⇒x1+x2=10,y1+y2=12

B(x1,y1) lies on the line 2x+3y=29

∴2x1+3y1=29 ----(1)

C(x2,y2) lies on the line x+2y=16,

∴x2+2y2=16 ----(2)

∴ putting x1,y1 in the form of x2,y2 in (1)

2(10−x2)+3(12−y2)=29 {x1=10−x2,y1=12−y2}

⇒20−2x2+36−3y2=29

⇒2x2+3y2=27 ----(3)

on subtracting (3) and (2) × 2

−y2=−5

y2=5

Putting y2in(2)

x2+2(5)=16

x2=6

x1=10−x2

=4

y1=12−5=7

Equation :

x2−x1x−x1=y2−y1y−y1

⇒2x−4=−2y−7

⇒−x+4=y−7

⇒x+y=11