find the value of 'a' such that PQ=QR where P,Qand R are the points whose coordinate are (6,1) (1,3) and (a,b) respectively
Answers
Step-by-step explanation:
DJ IDK if u want me there at like midnight and I was like oh
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Class 11
>>Applied Mathematics
>>Straight lines
>>Introduction
>>Find the value of x such th...
Question
Bookmark
Find the value of x such that PQ=QR where the coordinates of P,Q and R are (6,−1),(1,3) and (x,8) respectively.
Medium
Solution
verified
Verified by Toppr
Coordinate of point P,Q and R are P(6,-1),Q(1,3) and R(x,8)
Given, PQ=QR
So by distance formula we have,
Distance between two points =
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
PQ=
(6−1)
2
+(−1−3)
2
=
25+14
=
41
∴PQ
2
=41=QR
2
but, QR
2
=(x−1)
2
+25
41=x
2
+1−2x+25
⇒41=x
2
+1−2x+25
⇒x
2
−2x+26=41
⇒x
2
−2x−15=0
⇒x
2
−5x+3x−15=0
⇒x(x−5)+3(x−5)=0
⇒(x+3)(x−5)=0
⇒x=−3,5