if L , N and M are the points which divides the line segment A(-2,2) and B(2,8) , N being closer to B. Then the coordinates of M and N respectively are
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Answers
Answer:
Let
P,Q,R be the points that divide the line segment joining A(−2,2) and B(2,8) into four equal parts.
Since, Q is the mid-point of AB.
∴ Coordinates of Q are (2−2+
2,22+8)
I.e., (0,5)
Now, P divides AQ into two equal parts i.e., P is the mid-point of AQ
∴ Coordinates of P are (2−2+0,22+5)
I.e., (−1,27)
Again, R is the mid-point of QB.
∴ Coordinates of R are (20+2,/25+8)
İe., (1,21/3)
Hence, the coordinates of P,Q and R are (0,5),(−1,27) and (1,21/3).
Answer :
- The coordinates of L, M and N are ( 0, 5 ) , ( - 1 , 7/2 ) and ( 1 , 13/2 )
Solution :
Diagram
(-2,2) (2,8)
•-----------•------------•------------•------------•
A L M N B
Explanation
Let, L, M, N be the points that divide the line segment joining A(-2,2) and B(2,8) into four equal parts.
M is the midpoint of AB
A (-2,2) = (x1 , y1)
B (2,8) = (x1 , y2 )
Coordinates of M are [(x1 + x2)/2 , (y1 + y2)/2]
➝ [(-2 + 2 )/2 , (2 + 8 )/2]
➝ (0/2 , 10/2 )
➝ Coordinates of M are ( 0 , 5 )
Now, L divides AM into two equal parts
hence, L is midpoint of AM
A (-2,2) = (x1 , y1)
M (0,5) = (x1 , y2 )
Coordinates of L are [(x1 + x2)/2 , (y1 + y2)/2]
➝ [(-2+0)/2 , (2+5)/2 ]
➝ [ (-2)/2 , (7)/2 ]
➝ Coordinates of L are ( - 1 , 7/2 )
Again, N is the midpoint of MB
M ( 0,5 ) = (x1 , y1)
B (2,8) = (x2, y2)
Coordinates of N are [(x1 + y1)/2 , (x2 + y2 )/2 ]
➝ [(0 + 2)/2 , (5 + 8)/2]
➝ [2/2 , 13/2]
➝ ( 1 , 13/2 )
Hence, The coordinates of L, M and N are ( 0, 5 ) , ( - 1 , 7/2 ) and ( 1 , 13/2 )
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