Question

write the coordinate of the fourth vertex of a square when three of its veryices are given by (1,2) (5,2) (5,-2)​

Answer 1

Answer:

the coordinate of the fourth vertex are (1,-2) as shown in fig.

Answer 2

The coordinate of the fourth vertex are (1,-2).

Step-by-step explanation:

Consider the given vertices of square are A(1,2), B(5,2), C(5,-2)​.

We know that diagonals of a square are perpendicular bisector. So, midpoint of both diagonals are same.

Let the coordinate of the fourth vertex are D(a,b).

Midpoint of BD = Midpoint of AC

$(\dfrac{5+a}{2},\dfrac{2+b}{2})=(\dfrac{1+5}{2},\dfrac{2-2}{2})$

$(\dfrac{5+a}{2},\dfrac{2+b}{2})=(3,0)$

On comparing both sides.

$\dfrac{5+a}{2}=3$

$5+a=6$

$a=6-5=1$

The value of a is 1.

$\dfrac{2+b}{2}=0$

$2+b=0$

$b=-2$

The value of b is -2.

Therefore, the coordinate of the fourth vertex are (1,-2).

#Learn more

(2,1),(-1,2) and (1,0) are the coordinates of three vertices of a parallelogram.Find the fourth vertex

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