Question

What type of a quadrilateral do the points $A(2,2),B(7,3),C(11,1)$ and $D(6,6)$ taken in that order, form?

• A. Scalene quadrilateral
• B. Square
• C. Rectangle
• D. Rhombus

Answer 1

The correct option is A Scalene quadrilateral

Given that the point

$A(x_1,y_1)=(2,2),B(x_2,y_2)=(7,3),C(x_3,y_3)=(11,1)$ and $D(x_4,y_4)=(6,6)$ form a quadrilateral $ABCD$.

Its type will be (i) a scalene one, if $AC\ne BD$, (ii) a rectangle, if $AC=BD$.

We apply the distance formula, to get

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore AC=\sqrt{{(x_3-x_1)}^2+{(y_3-y_1)}^2}=\sqrt{{(11-2)}^2+{(1-2)}^2}$ units

$=\sqrt{82}$units and

$BD=\sqrt{{(x_4-x_2)}^2+{(y_4-y_2)}^2}=\sqrt{{(6-7)}^2+{(3-6)}^2}$ units

$=\sqrt{10}$ units

So, $AC\ne BD$

$\therefore ABCD$ is a scalene quadrilateral.

Also,

$AB=\sqrt{{(7-2)}^2+{(3-2)}^2}=\sqrt{26}$ units

$BC=\sqrt{{(11-7)}^2+{(1-3)}^2}=\sqrt{20}$ units

Thus, the sides are not equal. So, they does not represent a rhombus or a square.

Hence, only option A is correct.