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Abcd is a Parallelogram. If the Coordinates of A, B, C Are (−2, −1), (3, 0) and (1, −2) Respectively, Find the Coordinates of D.

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प्रश्न

ABCD is a parallelogram. If the coordinates of A, B, C are (−2, −1), (3, 0) and (1, −2) respectively, find the coordinates of D.

संक्षेप में उत्तर
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उत्तर

Let the coordinates of D is (x, y).
ABCD  is a parallelogram.
AB = DC 
We have,
\[\overrightarrow{AB} = \overrightarrow{DC} \]
\[ \Rightarrow 3 \stackrel\frown{i} - \left( - 2 \stackrel\frown{i} - \stackrel\frown{j} \right) = \left( \stackrel\frown{i} - 2 \stackrel\frown{j} \right) - \left( x \stackrel\frown{i} + y \stackrel\frown{j} \right)\]
\[ \Rightarrow 5 \stackrel\frown{i} + \stackrel\frown{j} = \stackrel\frown{i} \left( 1 - x \right) + \stackrel\frown{j} \left( - 2 - y \right)\]
\[ \Rightarrow 1 - x = 5\text{ and }1 = - 2 - y\]
\[ \Rightarrow x = - 4\text{ and }y = - 3\]
Hence, the coordinates of D is \[\left( - 4, - 3 \right)\]

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अध्याय 22: Algebra of Vectors - Exercise 23.4 [पृष्ठ ४३]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 22 Algebra of Vectors
Exercise 23.4 | Q 6 | पृष्ठ ४३

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