InterviewSolution
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InterviewSolution
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Student of a school are standing in rows and columns in their playground for a drill practice. A, B, C, D are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from eachl of the four students A, B, C and D? Ifso, what should be his position ? |
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Answer» Solution :Co-ordinates of A, B, C and D fron graph are A(3, 5), B(7, 9), C(11, 5) and D(7, 1). To find the shape of `SQUAREABCD` : `""AB^(2)=(7-3)^(2)+(9-5)^(2)=4^(2)+4^(2)=32` `rArr""AB=4sqrt(2)` units `""BC^(2)=(11-7)^(2)+(5-9)^(2)=(4)^(2)+(-4)^(2)=32` `rArr""BC=4sqrt(2)` units `""CD^(2)=(7-11)^(2)+(1-5)^(2)=(-4)^(2)+(-4)^(2)=32` `rArr""CD=4sqrt(2)` units `""DA^(2)=(7-3)^(2)+(1-5)^(2)=4^(2)+(-4)^(2)=32` `rArr""DA=sqrt(4^(2)(1+1))=4sqrt(2)` units `therefore""AB=BC=CD=DA=4sqrt(2)` units So, ABCD will be EITHER square or rhombus. Now, `"""DIAGONAL "AC=sqrt((11-3)^(2)+(5-5)^(2))` `rArr""AC=sqrt((8)^(2)+(0)^(2))""rArrAC=8` units and `"""diagonal "BD=sqrt((7-7)^(2)+(1-9)^(2))=sqrt((0)^(2)+(-8)^(2))=sqrt(8^(2))` `rArr""BD=8` units `therefore """Diagonal "AC="Diagonal "BD` So, given quadrilateral ABCD is a squre. The point which is equidistant from point A, B, C, D of a square ABCD will be at the intersecting point of diagonals and diagonals bisects each other. Hence, the required point O equidistant from A, B, C, D is mid-point of any diagonal `=((7+7)/(2), (9+1)/(2))=((14)/(2), (10)/(2))=(7, 5)`. Hence, the required point is (7, 5). |
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