Question

The points (-3, 5) and (3,5) are two verticles of a square. list all other order pairs that could be the other two verticles of the square.

Answer 1

( - 3, - 1 ), ( 3, - 1 ) / ( - 3, 11 ), ( 3, 11 )

Explanation:

Let us first consider the distance between points ( - 3, 5 ) and ( 3, 5 );

`( - 3, 5 ), ( 3, 5 )\\Distance = 3 + 3 = 6 units`

If these are points that are vertices of the square, it should be that the other 2 points are 6 units farther from these points;

`Distance = 6 units,\\( - 3, 5 ) - ( - 3, - 1 )\\( 3, 5 ) - ( 3, - 1 )`

`Distance = 6 units,\\( -3, 5 ) - ( - 3, 11 )\\( 3, 5 ) - ( 3, 11 )`

Let us confirm ( -3, - 1 ) and ( 3, - 1 ) are 6 units apart, respectively ( -3, 11 ) and ( 3, 11 ) to say they are the other two vertices;

`( - 3, - 1 ), ( 3, - 1 )\\Distance = 3 + 3 = 6 units`

`( -3, 11 ), ( 3, 11 )\\Distance = 3 + 3 = 6 units`

Thus, the possible vertices are ( - 3, - 1 ) and ( 3, - 1 ) or ( - 3, 11 ) and ( 3, 11 )

Answer 2

((-3,-1),(3,-1)),((-3,11),(3,11))

Explanation:

The distance between the two vertices is 6

So, add 6 and minus 6 to the y coordinates.