Three Dimensional Geometry Question 316
Question: Which of the following statement is true?
Options:
A) The point A(0, -1), B(2, 1), C(0, 3) and D(-2, 1) are vertices of a rhombus.
B) The points A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) are vertices of a square.
C) The points A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) are vertices of a parallelogram.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Here $ (a)A(0,-1),,B(2,1),,C(0,3),,D(-2,1) $ . For a rhombus all four sides are equal but the diagonal are not equal, we see $ AC=\sqrt{0+4^{2}}=4 $ , $ BD=\sqrt{4^{2}-0}=4 $ Since diagonals are equals therefore it is a square, not rhombus [b] Here $ AB=\sqrt{2^{2}+{{(-3)}^{2}}}=\sqrt{13},,BC $ $ =\sqrt{6^{2}+4^{2}}=\sqrt{52} $ Since $ AB\ne BC $ therefore it is not square. [c] In this case mid point of AC is $ ( \frac{4-2}{2},\frac{3-1}{2} ) $ or $ (1,1) $ Also mid-point of diagonal $ BD( \frac{1+1}{2},\frac{0+2}{2} ) $ or (1, 1) Hence the points are vertices of a parallelogram.
BETA
