Properties of rectangle :
Properties of square :
Properties of rhombus :
Properties of parallelogram :
Problem 1 :
Points P(4, 12), Q(9, 14), and R(13, 4) are three vertices of a rectangle. Find the coordinates of the fourth vertex S.
Solution:
Let the coordinate of the fourth vertex are S(a, b).
Midpoint of PR = Midpoint of QS
On comparing both sides,


So, the coordinates of the fourth vertex are (8, 2).
Problem 2 :
Find point D that makes ABCD a square where A(1, 4), B(2, 1), and C(3, 2).
Solution:
Let the coordinate of the fourth vertex are D(a, b).
Midpoint of AC = Midpoint of BD


So, the coordinates of the fourth vertex are (4, 3).
Problem 3 :
Points A(1, 2), B(3, 3) and D(6, 3) form three corners of a parallelogram. Find the fourth vertex, C.
Solution:
Let the coordinate of the fourth vertex are C(a, b).
Midpoint of AC = Midpoint of BD


So, the coordinates of the fourth vertex are (4, 2).
Problem 4 :
Find point P that makes PQRS a rectangle where Q(1, 5), R(2, 3) and S(2, 3).
Solution:
Let the coordinate of the fourth vertex are P(a, b).
Midpoint of PR = Midpoint of QS


So, the coordinates of the fourth vertex are (5, 1).
Problem 5 :
Find point S that makes PQRS a rectangle where P(6, 36), Q(30, 9), and R(12, 15).
Solution:
Let the coordinate of the fourth vertex are S(a, b).
Midpoint of PR = Midpoint of QS


So, the coordinates of the fourth vertex are (24, 12).
Mar 14, 24 10:44 PM
Mar 14, 24 10:12 AM
Mar 14, 24 09:52 AM