Question

The
square are 41,-6) and (5,4). Find the
opposite vertices of
coordinates of other two vertices​

Answer 1

Answer:

Draw line segment AB =4.2cm.

With B as the center and radius equal to 4.2cm, draw an arc.

Wth A as the center and radius equal to 6.5cm, draw another arc such that it intersects the previous arc at C.

Join points B,C, and A,C.

With A as the center and radius equal to 4.2cm, draw an arc.

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Answer 2

Step-by-step explanation:

ANSWER

Solution−

ABCDisasquare.

SoAB=BC=CD=DA&thediagonalsAC=BD..........(i).

Weshallapplydistanceformulatogettheabovelengths.

d=

(x

1

−x

2

)

2

+(y

1

−y

2

)

2

.

NowΔABCisarightonewithACashypotenuse(∠ABC=90

o

).

∴AC=

(5−1)

2

+(4+6)

2

units=

116

units=BD(byi)........(ii).

Weknowthatsideofasquare=

2

diagonal

.

∴AB=BC=CD=DA=

2

116

units=

58

units.........(iii).

Now,usingthedistanceformulad=

(x

1

−x

2

)

2

+(y

1

−y

2

)

2

,

AB

2

=BC

2

⟹(x

1

−5)

2

+(y

1

−4)

2

=(x

1

−1)

2

+(y

1

+6)

2

⟹8x

1

+20y

1

−4=0

⟹2x

1

+5y

1

−1=0

⟹y=

5

1−2x

1

........(iv).

∴AB

2

+BC

2

=AC

2

⟹(x

1

−5)

2

+(y

1

−4)

2

+58=116(fromii&iii)

⟹(x

1

−5)

2

+(y

1

−4)

2

=58

⟹(x

1

−5)

2

+(

5

1−2x

1

−4)

2

=58

⟹29x

1

2

−174x

1

−464=0

⟹x

1

2

−6x

1

−16=0

⟹(x

1

−8)(x

1

+2)=0

⟹x

1

=(8,−2).

So,from(iv),

y

1

=(

5

1−2×8

,

5

1−2(−2)

)=(−3,1).

∴B(x

1

,y

1

)=(8,−3)and(−2,1).