Question

The coordinate of the 4 vertex of the rectangle formed by (5,3)and (2,3) and(2,7) are​

Answer 1

Step-by-step explanation:

Lets say the coordinates of A, B, C and D in the coordinate region are

A are ( 0,0)

B are (2,0)

C are ( 0,3)

and D are ( x,y)

Now the fourth vertex is ABDC is

MP(BC) = MP(AD)

(2/2 , 3/2) =  (X/2 , Y/2)

Thus the coordinates of fourth vertex are (2,3).

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Answer 2

Given:

Three vertices of a rectangle whose coordinates are given as (5,3), (2,3) and (2,7).

To find:

The coordinates of the fourth vertex of the rectangle.

Solution:

Let the coordinates of the vertices be named as $A(5,3), B(2,3), C(2,7)$ and $D(x,y)$.

The $y$ coordinates of A and B are the same, i.e., $3$. Hence, they lie on the same line and form the breadth of the rectangle.

The $x$ coordinates of A and C are the same, i.e., $2$. Hence, they lie on the same line and form the length of the rectangle.

Now, a rectangle has four sides with the opposite sides being equal. Since AC is the length, BD is the other length of the rectangle. Since AB is the one breadth of the rectangle, the other breadth is CD.

When BD is the other length of the rectangle, the $x$ coordinate of D should be the same as that of point B, i.e., $5$.

When CD is the other breadth of the rectangle, the $y$ coordinate of D should be the same as that of point C, i.e., $7$.

Hence, the coordinates of D is $D(x,y)=D(5,7)$ which is the fourth vertex of the rectangle.

The coordinates of the fourth vertex of the rectangle are (5,7).