Question

18 points

Answer 1

Answer: The answer is (c) parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular.

Step-by-step explanation: The co-ordinates of the vertices of quadrilateral ABCD are given to be A(3,-5), B(5,-2), C(10,-4) and D(8,-7).

The lengths of the sides are as follows -

$\textup{AB}=\sqrt{(3-5)^2+(-5+2)^2}=\sqrt{4+9}=\sqrt13,\\\\\textup{BC}=\sqrt{(5-10)^2+(-2+4)^2}=\sqrt{25+4}=\sqrt{29},\\\\\textup{CD}=\sqrt{(10-8)^2+(-4)+7}^2=\sqrt{4+9}=\sqrt{13},\\\\\textup{DA}=\sqrt{(8-3)^2+(-7+5)^2}=\sqrt{25+4}=\sqrt{29}.$

Therefore, AB = CD  and  BC = DA.

Also, the slopes of the sides AB(m), BC(n), CD(o) and DA(p) are as follows

$m=\dfrac{2+5}{5-3}=\dfrac{3}{2},\\\\n=\dfrac{-4+2}{10-5}=-\dfrac{2}{5},\\\\o=\dfrac{-7+4}{8-10}=\dfrac{3}{2},\\\\p=\dfrac{-7+5}{8-3}=-\dfrac{2}{5}.$

For two lines to be perpendicular, the product of their slopes should be -1 and for them to be parallel, their slopes must be equal. So, here no two pair of lines are perpendicular. But, m = o and n = p and so, the opposite sides are parallel.   

Since the opposite sides are congruent and parallel, but not perpendicular, so the quadrilateral ABCD is a parallelogram.

Thus, the correct option is (c).

Answer 2

Answer: Parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular

Step-by-step explanation:

I got this right on my Quiz !