Question

Plzz give answer with full solution..​

Answer 1

Equation of two lines of rhombus=x-y+1,7x-y+5

since the slope is not eqaul,so we can say that both the lines are adjacent to each other

since both the lines are adjacent,they,will meet at a point

so, let's take out the first vertex

x-y+1=0....i)

7x-y-5=0....ii)

subtract i) from ii)

6x-6=0

x=1

y=2(by putting the value of x in i) eq.}

so,first vertex is (1,2)

now,slope of it's one of it's diagonal

=2+2/2=2

noww let eqaution of that line be 2x-y+c=0

put x=1 and y=2

c=3

so eqaution of this digonal is 2x-y+3=0

since Rhombus are perpendicular so seconddiagonal will be (-opposite of slope of the first diagonal)

so let another diagonal be,x+2y+c=0

put x=-1 and y=-2

c=5

so eqaution will be

x+2y+5=0

let one,of the vertex be (x,y)

(x+1)/2=-1

x=-3

(y+2)/2=-2

y=-2

so, another vertex=(-3,-2)

since,the second diagonal x+2y+5=0,will intersect,at,the line,(x-y+1) and(7x-y-5)

so

using this will will take out another two vertex

x-y+1=0.....i)

x+2y+5=0..ii)

subtract,I) from ii)

3y=-4

y=-4/3

x=1/3

so, third vertex=(1/3,-4/3)

7x-y-5=0...III)

x+2y+5=0..iv)

multiply eqaution III) be 2

14x-2y-10=0..v)

add iv) and v

15x-5=0

x=1/3

put this in ,III)

we get

y=-8/3

so last vertex=(1/3,-8/3)

Answer 2

Answer:

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