Question

Question 6
The points A(4,3), B(6,4), C(5,-6) and D(-3,5) are vertices of a parallelogram.

Answer 1

False,
Now, distance between A(4,3) and B(6,4):
$AB=\sqrt{(6-4{)}^2+(4-3{)}^2}=\sqrt{2^2+1^2}=\sqrt{5}\left[\begin{array}{c}\because \text{distance between the points}(x_1,y_1)and(x_2,y_2),d\\ =\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}\end{array}\right]\text{Distance between B(6,4) and C(5,-6),}BC=\sqrt{(5-6{)}^2+(-6-4{)}^2}=\sqrt{(-1{)}^2+(-10{)}^2}\sqrt{1+100}=\sqrt{101}\text{Distance between C(5,-6) and D(-3,5),}CD=\sqrt{(-3-5{)}^2+(5+6{)}^2}=\sqrt{(-8{)}^2+{11}^2}=\sqrt{64+121}=\sqrt{185}\text{Distance between D(-3,5) and A(4,3),}DA=\sqrt{(4+3{)}^2+(3-5{)}^2}=\sqrt{7^2+(-2{)}^2}=\sqrt{49+4}=\sqrt{53}$
In parallelogram, opposite sides are equal. Here, we see that all sides AB, BC, CD and DA are of different length.
Hence, given vertices are not the vertices of a parallelogram .