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Distance Formula

Are the point...

Question

Are the points given below collinear? If, state which point lies between the other two $d (P, Q) = 11, d (Q, R) = 6.5, d (P, R) = 4.5$

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Solution

$d (P, Q) > d (Q, R) > d (P, R)$
$P Q = 11$ units. $Q R = 6.5$ units and $P R = 4.5$ units.
We observe that $6.5 + 4.5 = 11.0$ units
$∴ Q R + P R = P Q$
Thus, the points $P, Q, R$ are collinear.
And $R$ lies between $P$ and $Q$

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Q. If d(Q,R) = 25, d(P,R) = 45, What must be the value of d(P,Q) if the points P,Q,R are on the same straight line and Q lies in between P and R

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5 and 6 respectively. State with reason whether the following statements are true or false.

(i) d(P,Q) + d(Q,R) = d(P,R)
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d(P,R) = d(Q,R)

From the information given below, find which of the point is between the other two. If the points are not collinear, state so.

(i) d(P, R) = 7, d(P, Q) = 10, d(Q, R) = 3

(ii) d(R, S) = 8, d(S, T) = 6, d(R, T) = 4

(iii) d(A, B) = 16, d(C, A) = 9, d(B, C) = 7

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(v) d(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 8

(vi) d(D, E) = 5, d(E, F) = 8, d(D, F) = 6

Answer the following questions.

(i) If A - B - C and d(A,C) = 17, d(B,C) = 6.5 then d(A,B) = ?

(ii) If P - Q - R and d(P,Q) = 3.4, d(Q,R)= 5.7 then d(P,R) = ?

Q. If P - Q - R and d(P, Q) = 10 units, d(P, R) = 20 units, then d(Q, R) = ________ units.

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