InterviewSolution
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InterviewSolution
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Find the distance between the following points : (i) (3, 4) and (5, 2) (ii) (0, 2) and (4, -1) (iii) (a, 2a) and (-a, -2a) (iv) (4, -3) and (- 6, 5) |
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Answer» (i) Distance between the points (3, 4) and (5, 2) ` " "=sqrt((x_(2)-x_(1))^(2)+( y_(2)-y_(1))^(2))=sqrt((5-3)^(2)+(2 -4)^(2))` `" "=sqrt(4+4)=sqrt(8)=2sqrt(2)` units (ii) Distance between the points (0, 2) and ( 4, -1) `" "=sqrt((x_(2)-x_(1))^(2 )+(y_(2) -y_(1))^(2))=sqrt((4-0)^(2)+(-1-2)^(2))` `" "=sqrt((4)^(2)+(-3)^(2))=sqrt(16+9)=sqrt(25)= 5` units (iii) Distance between the points (a, 2a) and ( - a, -2a) `" "=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))=sqrt((-a -a)^(2)+(- 2a -2a)^(2))` `" " =sqrt((-2a)^(2)+(-4a)^(2))=sqrt(4a^(2)+16a^(2))=sqrt(20a^(2))=2sqrt(5)a` units (iv) Distance between the points (4, -3) and (-6, 5) ` " "=sqrt((x_(2)-x_(1))^(2)+( y_(2)-y_(1))^(2))=sqrt((-6-4)^(2)+(5+3)^(2))` ` " "=sqrt((-10)^(2 )+(8)^(2))=sqrt(100+64)=sqrt(164)=2sqrt(41)` units |
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