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3. From the information given below, find which of the point is between the other two. If the points are not collinear, state so. (i) \( d( P , R )=7, \quad d( P , Q )=10, \quad d( Q , R )=3 \) (ii) \( d( R , S )=8, \quad d( S , T )=6, \quad d( R , T )=4 \) (iii) \( d( A , B )=16, \quad d( C , A )=9, \quad d( B , C )=7 \) (iv) \( d( L , M )=11, \quad d( M , N )=12, \quad d( N , L )=8 \) (y) \( d( X , Y )=15, \quad d( Y , Z )=7, \quad d( X , Z )=8 \)(vi) \( d( D , E )=5 \) \( d( E , F )=8, \quad d( D , F )=6 \) |
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Answer» answers 1) d(P, Q) = 10 d(P, R) + d(Q, R) = 7+3 = 10 d(P, Q) = d(P, R) + d(Q, R) therefore, point R is between the points P and Q i. e., P-R-Q Or Q-R-P.points P, R, Q are collinear. 2) d(R, S) = 8 d(S, T) + d(R, T) = 6+4 = 10 d(R, S) ≠ d(S, T) + d(R, T) therefore, the given points are not collinear. 3) d(A, B) = 16 d(C, A) + d(B, C) = 9+7= 16 d(A, B) = d(C, A) + d(B, C) point C is between the points A and B i. e., A-C-B Or B-C-A.. points A, C, B are collinear. i can't finish the answers as I don't have time but when I do I will. |
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