Question

A triangle is formed by the lines
x-2y+8, 2x-y+1=0 and x-5y+14=0.
Find graphically the co ordinates of the vertices of the triangle​

Answer 1

Answer:

(2,5);(1,3);(-4,2)

Step-by-step explanation:

Well, the vertices of the triangle are the intersecting points of 2 lines taken at a time from the given three lines

If the lines are l, m, n in the order given in the question

Then, intersection of lines

1. l and m = (2,5)
2. m and n = (1,3)
3. n and l = (-4,2)

So these are the vertices.

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Answer 2

Answer:

Coordinates of vertices of triangle are (2,5),(1,3) and (-4,2)

Step-by-step explanation:

Given triangle is formed by the lines  x-2y+8, 2x-y+1=0 and x-5y+14=0.

x-2y+8=0 --->(1)

2x-y+1=0 --->(2)

x-5y+14=0 --->(3)

solving eq(1) and eq(2)

eq(1)*2⇒2x-4y=-16

eq(2)    ⇒2x-y=-1

eq(1)*2-eq(2)=>  -3y=-15

y=5

x=2y-8=10-8=2

point is(2,5)

solving eq(2) and eq(3)

eq(2)=>2x-y=-1

eq(3)*2=>2x-10y=-28

2-3*2=>9y=27

y=3

x=(y-1)/2=2/2=1

point is(1,3)

solving eq(3) and eq(1)

eq(1)=>x-2y=-8

eq(3)=>x-5y=-14

eq(1)-eq(3) =>3y=6

y=2

x=-8+4=-4  

point is (-4,2)

Coordinates of vertices of triangle are (2,5),(1,3) and (-4,2)