Three vertices of a rectangle ABCD are A(3,1),B(-3,1)and C(-3,3).Plot these points on a graph paper and find the coordinates of the fourth vertex D. Also, find the area of rectangle ABCD.
Answers
→ by looking at the graph we see that coordinates of D are (3,3)
→ DC = 6 units. [ in graph]
→ BC= 2 units.
→ therefore, area of rectangle = L X B
= 6 X 2 = 12 cm
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hope it helps you ☺
Given : Three vertices of a rectangle ABCD are A(3,1), B(-3,1), C(-3,3)
To find : Plot these points and find the coordinates of the fourth vertex.
Solution:
A(3,1), B(-3,1), C(-3,3)
Let say D = (x , y)
AD = BC
=> √(x - 3)² +(y - 1)² = √(-3 + 3)² + ( 1 - 3)²
=> (x - 3)² +(y - 1)² = 4
=> x² + y² - 6x - 2y = -6
CD = AB
=> √(x +3)² +(y -3)² = √(-3 - 3)² + (1 - 1)²
=> (x +3)² +(y - 3)² = 36
=> x² + y² + 6x -6 y = 18
=> 12x - 4y = 24
=> 3x - y = 6
BD=AC
=> (x +3)² +(y -1)² = 36 + 4
(x +3)² +(y - 3)² = 36
=>(y - 1)² - (y - 3)² = 4
=> 4y - 8 = 4
=> y =3
3x - y = 6
=> 3x =9
=> x = 3
( 3, 3) is the coordinates of the fourth vertex.
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