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CBSE Class 11-science Answered

The midpoints of the sides of a triangle are (1,5,-1), (0,4,-2) and (2,3,4) find its vertices.

A student takes honesty, truthfulness and complacency as the three sides of the triangle. Which side of the triangle should we prefer to take?

Asked by Topperlearning User | 15 Nov, 2016, 01:29: AM
Expert Answer

Let coordinates of vertices be (x1,y1,z1 ), B(x2,y2,z2) C(x3,y3z3)

 

Coordinates of D are open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction comma fraction numerator z subscript 1 plus z subscript 2 over denominator 2 end fraction close parentheses equals open parentheses 1 comma 5 comma negative 1 close parentheses
rightwards double arrow x subscript 1 plus x subscript 2 equals 2 space comma space y subscript 1 plus y subscript 2 equals 10 space comma space z subscript 1 plus z subscript 2 equals negative 2

Coordinates of E areopen parentheses fraction numerator x subscript 2 plus x subscript 3 over denominator 2 end fraction comma fraction numerator y subscript 3 plus y subscript 2 over denominator 2 end fraction comma fraction numerator z subscript 3 plus z subscript 2 over denominator 2 end fraction close parentheses equals open parentheses 0 comma 4 comma negative 2 close parentheses
rightwards double arrow x subscript 3 plus x subscript 2 equals 0 space comma space y subscript 3 plus y subscript 2 equals 8 space comma space z subscript 3 plus z subscript 2 equals negative 4

Coordinates of F are (2,3,4) = open parentheses fraction numerator x subscript 1 plus x subscript 3 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 3 over denominator 2 end fraction comma fraction numerator z subscript 1 plus z subscript 3 over denominator 2 end fraction close parentheses equals open parentheses 2 comma 3 comma 4 close parentheses
rightwards double arrow x subscript 1 plus x subscript 3 equals 4 space comma space y subscript 1 plus y subscript 3 equals 6 space comma space z subscript 1 plus z subscript 3 equals 8

left parenthesis x subscript 1 plus x subscript 2 right parenthesis plus left parenthesis x subscript 2 plus x subscript 3 right parenthesis plus left parenthesis x subscript 1 plus x subscript 2 right parenthesis equals 6
rightwards double arrow x subscript 1 plus x subscript 2 plus x subscript 3 equals 3 space space
rightwards double arrow 2 plus x subscript 3 equals 3 space space space space space space space space space space space space x subscript 1 plus 0 equals 3 space space space space space space x subscript 2 plus 4 equals 3
rightwards double arrow x subscript 3 equals 1 space space space space space space space space space space space space space space space space space space x subscript 1 equals 3 space space space space space space space space space space space space x subscript 2 equals negative 1 space space space space

left parenthesis y subscript 1 plus y subscript 2 right parenthesis plus left parenthesis y subscript 2 plus y subscript 3 right parenthesis plus left parenthesis y subscript 1 plus y subscript 2 right parenthesis equals 24
rightwards double arrow y subscript 1 plus y subscript 2 plus y subscript 3 equals 12
rightwards double arrow 10 plus y subscript 3 equals 12 space space space space space space space space space space space space y subscript 1 plus 8 equals 12 space space space space space space y subscript 2 plus 6 equals 12
rightwards double arrow y subscript 3 equals 2 space space space space space space space space space space space space space space space space space space space space space space space space y subscript 1 equals 4 space space space space space space space space space space space space y subscript 2 equals 6 space space


left parenthesis z subscript 1 plus z subscript 2 right parenthesis plus left parenthesis z subscript 2 plus z subscript 3 right parenthesis plus left parenthesis z subscript 1 plus z subscript 2 right parenthesis equals 2
rightwards double arrow z subscript 1 plus z subscript 2 plus z subscript 3 equals 1
rightwards double arrow negative 2 plus z subscript 3 equals 1 space space space space space space space space space space space space z subscript 1 minus 4 equals 1 space space space space space space z subscript 2 plus 8 equals 1
rightwards double arrow z subscript 3 equals 3 space space space space space space space space space space space space space space space space space space space space space space space space z subscript 1 equals 5 space space space space space space space space space space space space z subscript 2 equals negative 7 space space
V e r t i c e s space o f space t h e space t r i a n g l e space a r e space left parenthesis 3 comma 4 comma 5 right parenthesis space comma space left parenthesis negative 1 comma 6 comma negative 7 right parenthesis space comma space left parenthesis 1 comma 2 comma 3 right parenthesis

Honesty and Truthfulness

Answered by | 15 Nov, 2016, 03:29: AM
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