If P-1-4- Q-9-2- and R-5-1- are collinear thenP lies between Q and RQ lies between P and RR lies between P and Qnone of these

Question

Toppr Admin · Accepted Answer

PQ -xA0-x221A-1-x2212-9-2-4-2-2-10QR -xA0-x221A-9-x2212-5-2-x2212-2-x2212-1-2-5PR -xA0-x221A-1-x2212-5-2-4-x2212-1-2-5-x2234-PQ-PR-RQTherefore R lies between P and Q

If P(1,4), Q(9,-2), and R(5,1) are collinear then
P lies between Q and R
Q lies between P and R
R lies between P and Q
none of these

PQ = $\sqrt{{(1 - 9)}^{2} + {(4 + 2)}^{2}} = 10$
QR = $\sqrt{{(9 - 5)}^{2} + {(- 2 - 1)}^{2}} = 5$
PR = $\sqrt{{(1 - 5)}^{2} + {(4 - 1)}^{2}} = 5$
$∴ P Q = P R + R Q$
Therefore R lies between P and Q

If P(1,4), Q(9,-2), and R(5,1) are collinear thenP lies between Q and RQ lies between P and RR lies between P and Qnone of these

PQ = √(1−9)2+(4+2)2=10QR = √(9−5)2+(−2−1)2=5PR = √(1−5)2+(4−1)2=5∴PQ=PR+RQTherefore R lies between P and Q

If P(1,4), Q(9,-2), and R(5,1) are collinear then
P lies between Q and R
Q lies between P and R
R lies between P and Q
none of these

PQ = $\sqrt{{(1 - 9)}^{2} + {(4 + 2)}^{2}} = 10$
QR = $\sqrt{{(9 - 5)}^{2} + {(- 2 - 1)}^{2}} = 5$
PR = $\sqrt{{(1 - 5)}^{2} + {(4 - 1)}^{2}} = 5$
$∴ P Q = P R + R Q$
Therefore R lies between P and Q