The line joining A (2, -7) and B(6, 5) is divided into 4 equal parts by the points P,Q and R such that AQ = RP = QB. The midpoint of PR is

Question

The line joining A (2, -7) and B(6, 5) is divided into 4 equal parts by the points P,Q and R such that AQ = RP = QB. The midpoint of PR is  (A) (4,-1) (B) (8,-2) (C) (4,12) (D) (-8,1)

Tardigrade Admin · Accepted Answer

Given that, <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c6de578cd79ebf2dafe2e5473d747137-.png" /> A P=P Q=Q R=R B and A Q=R P=Q B Since, A Q=Q B, that means Q is the mid point of A B=[(2+6/2), (-7+5/2)]=(4,-1) Mid point of P R=(4,-1) [∵ P Q=Q R]

Q. The line joining $A (2, - 7)$ and $B (6, 5)$ is divided into $4$ equal parts by the points $P, Q$ and $R$ such that $A Q = RP = QB$ . The midpoint of $PR$ is _______

(4,-1)

(8,-2)

(4,12)

(-8,1)

Given that,

$A P = PQ = QR = RB$
and $A Q = RP = QB$
Since, $A Q = QB$ , that means $Q$ is the mid point of
$A B = [\frac{2 + 6}{2}, \frac{- 7 + 5}{2}] = (4, - 1)$
Mid point of $PR = (4, - 1)$
$[∵ PQ = QR]$

Q. The line joining A(2,−7) and B(6,5) is divided into 4 equal parts by the points P,Q and R such that AQ=RP=QB. The midpoint of PR is _______