Three vertices of a rectangle ABCD are A(4,-2), B(-3,-2), C(-3,1). Plot these points and f find the coordinates of the fourth vertex.
Answers
Step-by-step explanation:
the fourth coordinate will be
(4,1)
Given : Three vertices of a rectangle ABCD are A(4,-2), B(-3,-2), C(-3,1)
To find : Plot these points and find the coordinates of the fourth vertex.
Solution:
A(4,-2), B(-3,-2), C(-3,1).
Let say D = (x , y)
AD = BC
=> √(x - 4)² +(y + 2)² = √(-3 + 3)² + ( 1 + 2)²
=> (x - 4)² +(y + 2)² = 9
=> x² + y² - 8x + 4y = -11
CD = AB
=> √(x +3)² +(y -1)² = √(-3 - 4)² + (-2 + 2)²
=> (x +3)² +(y - 1)² = 49
=> x² + y² + 6x -2 y = 39
=> 14x - 6y = 50
=> 7x - 3y = 25
AC = BD
=> (x +3)² +(y + 2)² = 49 + 9
(x +3)² +(y - 1)² = 49
=> (y + 2)² - (y - 1)² = 9
=> 6y + 3 = 9
=> y = 1
7x - 3y = 25
=> 7x = 28
=> x = 4
( 4, 1) is the coordinates of the fourth vertex.
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