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(x_{1}, y_{1}) and B(x_{2}, y_{2}) is

AB = √[(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} ]

Now, as

PQ = QR

√[(5 - 0)^{2} + (- 3 - 1)^{2}] = √[(0 - x)^{2} + (1 - 6)^{2}]

= √x^{2} + 25

41 = x^{2} + 25

x^{2} = 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 :

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