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निर्देशांक ज्यामिति

Question
CBSEHHIMAH10010051

बिंदुओं A(-2, 2) और B(2, 8) को जोड़ने वाले रेखाखंड AB को चार बराबर भागों में विभाजित करने वाले बिंदुओं के निर्देशांक ज्ञात कीजिए।

Solution

(i) P बिंदु के लिए:

यहाँ, m1 = 1, m2 = 3
       x1 = -2, y2 = 2
       x2 = 2, y2 = 8
P के निर्देशांक:
       straight x subscript 1 space equals space fraction numerator 1 space straight x space 2 space plus space 3 space straight x space left parenthesis negative 2 right parenthesis over denominator 1 space plus space 3 end fraction space equals space fraction numerator 2 space minus space 6 over denominator 4 end fraction space equals space minus 4 over 4 space equals space minus 4
straight y subscript 1 space equals space fraction numerator 1 space straight x space 8 space plus space 3 space straight x space 2 over denominator 1 space plus space 3 end fraction space equals space fraction numerator 8 space plus space 6 over denominator 4 end fraction space equals space 14 over 2 space equals space 7 over 2
 P(x1, y1) = open parentheses negative 1 comma space 7 over 2 close parentheses
Q बिंदु के लिए:

यहाँ   m1 = 2, m2 = 2
        x1 = -2, y1 = 2
        x2 = 2, y2 = 8
Q के निर्देशांक:
       straight x subscript 1 space equals space fraction numerator 2 space straight x space 2 space plus space 2 space straight x space left parenthesis negative 2 right parenthesis over denominator 2 space plus space 2 end fraction space equals space fraction numerator 4 space minus space 4 over denominator 2 end fraction space equals space 0 over 2 space equals space 0
straight y subscript 1 space equals space fraction numerator 2 space straight x space 8 space plus space 2 space straight x space 2 over denominator 2 space plus space 2 end fraction space equals space fraction numerator 16 space plus space 4 over denominator 4 end fraction space equals space 20 over 4 space equals space 5
Q(x1, y1) = (0, 5)
R बिंदु के लिए:

यहाँ, m1 = 3, m2 = 1
       x1 = -2, y1 = 2
       x2 = 2, y2 = 8
R के निर्देशांक:
        straight x subscript 1 space equals space fraction numerator 3 space straight x space 2 space plus space 1 space straight x space left parenthesis negative 2 right parenthesis over denominator 3 space plus space 1 end fraction space equals space fraction numerator 6 space minus space 2 over denominator 4 end fraction space equals space 4 over 4 space equals space 1
straight y subscript 1 space equals space fraction numerator 3 space straight x space 8 space plus space 1 space straight x space 2 over denominator 3 space plus space 1 end fraction space equals space fraction numerator 24 space plus space 2 over denominator space 4 end fraction space equals space 26 over 4 space equals space 13 over 2
R(x1, y1) = open parentheses 1 comma space 13 over 2 close parentheses

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