Consider a quadrilateral A B C D (A quadrilateral is a closed figure with four straight sides) whose sides are A B , B C , C D and A D . The side A B of the quadrilateral is 15 units above the X − axis and is parallel to X − axis.The side C D lies on the X − axis. The other sides i.e., A D is parallel to side B C and the equation of the diagonal B D is 26 y − 15 x = 0 . What is the length of the diagonal A C , if the coordinates of A are ( 9 , 15 ) ?
Answers
Given : a quadrilateral A B C D
The side A B of the quadrilateral is 15 units above the X − axis and is parallel to X − axis
The side C D lies on the X − axis
A D is parallel to side B C and the equation of the diagonal B D is 26 y − 15 x = 0 .
the coordinates of A are ( 9 , 15 )
To Find : length of the diagonal A C
Solution:
The side A B of the quadrilateral is 15 units above the X − axis is parallel to X − axis.
=> Equation of line AB is y = 15
The side C D lies on the X − axis
=> Equation of CD is y = 0
AD is parallel to side B C
equation of the diagonal BD is 26 y − 15x = 0
26 y − 15x = 0 , y = 15
=> x = 26
Hence B = ( 26 , 15)
26 y − 15x = 0 , y = 0
=> x = 0
Hence D = ( 0 , 0)
Diagonals of parallelogram bisect each other
BD is diagonal hence mid point of BD = ( 26 + 0)/2 , ( 15 + 0)/2
= (13 , 7.5)
Coordinate of A = ( 9 , 15)
Coordinate of C = ( x , 0)
Mid point of AD = ( 9 + x)/2 , ( 15 + 0)/2
13 = (9 + x)/2
=> x = 17
Hence C = ( 17 , 0)
Coordinate of A = ( 9 , 15)
Coordinate of C = ( 17 , 0)
Length of Diagonal = √(17 - 9)² + 8²
= 17 unit
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