Question

The three vertices of a rhombus taken in order are(2,-1),(3,4)&(-2,3).Find the fourth vertex

Answer 1

hope it helps.........

Answer 2

Answer: (-3, -2)

Step-by-step explanation:

Let ABCD is a rhombus as shown in below figure and (x,y) is the coordinate of fourth vertex

Now as we know diagonals of a rhombus bisect each other

Therefore O is the midpoint of AC and BD

By mid point formula= $(x,y )= (\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2} )$

Mid point of AC = $(a,b)= (\dfrac{2+(-2) }{2}, \dfrac{-1+3}{2} )=( 0, 1 )$  ---(i)

Mid point of BD =$(a,b)= (\dfrac{x+3 }{2}, \dfrac{4+y}{2} )$ ---(ii)

from i and ii we get  

$( 0, 1 )=(\dfrac{x+3 }{2}, \dfrac{4+y}{2} )\\\\\Rightarrow0=\dfrac{x+3 }{2} \text{ and } 1=\dfrac{4+y}{2}\\\\\Rightarrow  x=-3 \text{ and } y= -2$

Hence the fourth vertex is (-3, -2)