ABCD is a square in which A lies on
positive Y-axis and B lies on the positive
X-axis. If D is the point (12, 17), then the
coordinate of C is
Answers
Given : ABCD is a square in which A lies on positive Y-axis and B lies on the positive X-axis. If D is the point (12, 17),
To find : the coordinate of C is
Solution:
A lies on positive Y-axis
A = ( 0 , y)
B lies on the positive X-axis
B = ( x , 0)
D = ( 12 , 17 )
Slope of AB = = - y/x
Slope of AD = (17 - y)/12
Slope of AB * Slope of AD = - 1
=> -(y/x) (17 - y)/12 = -1
=> 17 - y = 12x/y
AB = √x² + y²
AD = √12² + (17 - y )²
=>AD = √12² + (12x/y )²
=>AD = (12/y) √y² + x²
AB = AD
=> √x² + y² = (12/y) √y² + x²
=> 12 = y
17 - y = 12x/y
=> 17 - 12 = 12x/12
=> x = 5
A = ( 5 , 0)
B = (0 , 12)
C = (h , k)
D = 12 , 17
Slope of AD = 5/12
Slope of BC = k/(h - 5)
Slope of AD = Slope of BC
=> 5/12 = k/(h - 5)
=> 5h - 25 = 12k
=> 5h - 12k = 25 Eq1
Slope of AB = -12/5
Slope of CD = ( k - 17)/(h - 12)
Slope of AB = Slope of CD
=> -12/5 = ( k - 17)/(h - 12)
=> -12h + 144 = 5k - 85
=> 12h + 5k = 229 Eq2
5 * Eq1 + 12 * eq2
=> 25h + 144h = 125 + 2748
=> 169h = 2873
=> h = 17
5h - 12k = 25
=> 85 - 12k = 25
=> 12k = 60
=> k = 5
( 17 , 5) is the coordinate of C
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