Question

Find the fourth vertex of a rectangle whose three vertices taken in order are (4, 1 )(7,4) and (13, - 2)

Answer 1

Let rectangle be ABCD and the point A is 4,1 ; B is 7,4; C is 13, -2 and D is a,b

For a rectangle, mid point of diagonal are same.

midpoint of AC = 4+13 /2 , 1-2 /2 = 17/2, -1/2

midpoint of BD = a+7 /2 , b+4/2

a+7 /2 =17/2

a+7=17

a=10

similarly, b+4 / 2 = -1/2

b+4=-1

b = -5

The fourth co-ordinate of rectangle is (10,-5)


Mark me as a Brainliest.

Answer 2

Let the rectangle be ABCD.

A = ( 4,1 )

B = ( 7.4 )

C = ( 13,-2 )

Let D = ( p,q )

Diagonals are AC and BD

Midpoint of AC

AC = x = ( 4 + 13 ) / 2 , y = ( 1 - 2 ) / 2

= > x = 17 / 2 . y = - 1 / 2

Midpoint of BD

BD = x = ( p + 7) / 2 , y = ( q + 4 ) / 2

Midpoint of BD = Midpoint of AC

= > ( p + 7 ) / 2 = 17 / 2

= > p + 7 = 17

= > p = 17 - 7

= > p = 10

= > ( q + 4 ) / 2 = - 1 / 2

= > q + 4 = - 1

= > q = - 1 - 4

= > q = - 5

The coordinate is p , q

= > ( 10 , - 5 )

ANSWER :

( 10 , - 5 )