Q. 94.0( 293 Votes )
If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR
Answer :
We know, By distance formula distance between two coordinates A(x1, y1) and B(x2, y2) is
AB = √[(x2 - x1)2 + (y2 - y1)2 ]
Now, as
PQ = QR
√[(5 - 0)2 + (- 3 - 1)2] = √[(0 - x)2 + (1 - 6)2]
= √x2 + 25
41 = x2 + 25
x2 = 16
x = ± 4
Hence, point R is (4, 6) or ( - 4, 6).
When point R is (4, 6)
PR = [(5 - 4)2 + (-3 - 6)2]1/2
= 
= 
QR = [(0 - 4)2 + (1 - 6)2]1/2
= 
= 
When point R is (- 4, 6),
PR = [(5 + 4)2 + (-3 - 6)2]1/2
= 
= 9
QR = [(0+ 4)2 + (1 - 6)2]1/2
= 
= 
Rate this question :
Section Formula30 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE Questions29 mins
Smart Revision | Become a Master in Coordinate Geometry54 mins
Distance Formula and Section Formula44 mins
NCERT | Quiz on Section Formula43 mins
Champ Quiz | Coordinate Geometry Problems38 mins
Quiz | Solving Important Questions on Section Formula54 mins
NCERT Solutions of Distance Formula43 mins
Imp. Qs. on Distance Formula68 mins
Using distance formula, examine whether the following sets of points are collinear?
(0, 0), (9, 6), (3, 2)
KC Sinha - MathematicsProve that the distance between the points (a + rcosθ, b + rsinθ) and (a, b) is independent of θ.
KC Sinha - MathematicsUsing distance formula, examine whether the following sets of points are collinear?
(5, 1), (1, - 1), (11, 4)
KC Sinha - Mathematics