Answer :

Formula used:


Let A, B, C and D represent the points (6, 1), (8, 2), (9, 4) and (p, 3)


Distance of AB


AB = √ ((8 – 6))2 + (2 – 1)2)


AB = √ ((2)2 + (1)2)


AB = √ (4 + 1)


AB = √ 5


Distance of CD


CD = √ ((p – 9)2 + (3 – 4)2)


CD = √ ((p – 9)2 + (1)2)


CD = √ (p2 + 81 – 18p + 1)


CD = √ p2 – 18p + 82


i.e., The opposite sides are equal.


AB = CD


√5 = √ p2 – 18p + 82


Squaring both sides


5 = p2 – 18p + 82


p2 – 18p + 82 – 5 =0


p2 – 18p + 77 = 0


p2 – 11p – 7p + 77 = 0


p(p – 11) – 7(p – 11)= 0


(p – 11)(p – 7) = 0


p – 11 = 0 or p – 7 = 0


p = 11 or p = 7


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the distanceTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I

Show that the folTamilnadu Board Math Term-I