Question

The centre of a square ABCD is located at (2, 3), and the vertex D is located at (5, 6). The coordinates of the vertex exactly opposite to D are​
with explanation

Answer 1

Answer:

A (-1, 0)

Step-by-step explanation:

IF O(2, 3) IS THE CENTER OF SQUARE AND D(5, 6)IS ONE OF ITS VERTEX THEN ITS OPPOSITE VERTEX WILL BE B

IT MAKES A LINE 'BD' WITH ITS MID POINT O

Let the coordinates of point B be(x,y)

D(5,6) ; O(2,3); B(x, y)

5+x/2 =2 ; 6+y/2 = 3

5+x=4 ; 6+y = 6

x=4-5 ; y= 6-6

x= -1 ; y= 0

so coordinates of B(x, y) = B(-1,0)

Answer 2

Given:

A square ABCD with center (2,3) and a vertex D with coordinates(5,6).

To Find:

The coordinates of the vertex of the square which is exactly opposite to the vertex D.

Procedure:

1. Given (2,3) is the center of the square ABCD. (5,6) are the coordinates of vertex D.

2. From the properties of 2-D geometry, The center of the square is the midpoint of the opposite vertexes.

• Let PQRS be a square with points as P(x1,y1),Q(x2,y2),R(x3,y3), and S(x4,y4). Let PR and QS be the diagonals of the square.
• The center of the square is given by the expression $($ $\frac{x1+x3\\}{2}$,$\frac{y1+y3}{2}$$)$.
• The center of the square can also be obtained by taking the midpoints of the other two sides i.e, $( \frac{x2+x4}{2} ,\frac{y2+y4}{2} )$ .

3. Using the above formula, we can obtain the coordinates of the vertex opposite to the vertex at D.

=> let the coordinates of the vertex opposite to D be x,y.

=> Center (2,3) = [(5+x)/2 , (6+y)/2]

=> x = 4-5, y = 6-6,

=> x = -1 , y = 0.  

Therefore the coordinates of the vertex of the square which is opposite to the vertex D is (-1,0). Hence, Option A is correct.