Question

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​

Answer 1

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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