Question

The fourth vertex of a rectangle whose three vertices taken in order are (4,1) , (7,4) , (13,-2) is ?

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)

Answer 2

There are three vertices of a rectangle, namely: A (−4,5), B (−4,2), C (3,2). This question forms part of Coordinate Geometry.

let the fourth vertex be D(a,b)

in rectangle mid points of the diagonals are same

mid point of BD = mid point of AC

[(a+7)/2,(b+4)/2] = [(4+13)/2,(1-2)/2] = (17/2,-1/2)

(a+7)/2 = 17/2 and (b+4)/2 = -1/2

a+7 = 17, and b+4 = -1

a = 17-7 =10, and b = -1-4 = -5

fourth vertex D is (10,-5)