Question

Four vertices of a quadrilateral are W(4,2), X(5,0), Y(7,1), and Z(5,4). Choose the incorrect option about the new quadrilateral formed if it is being compared to the given quadrilateral in the following image.

• A. $\overline{AB}=\overline{WX}$
• B. $\angle DAC=\angle ZYX$
• C. $\overline{DC}=\overline{ZY}$
• D. $\overline{AD}=\overline{WZ}$

Answer 1

The correct option is B $\angle DAC=\angle ZYX$

Plot the quadrilateral WXYZ. Let's place the four points of the quadrilateral at the four respective coordinates W(4,2), X(5,0), Y(7,1), and Z(5,4).

The graph we get is:


From the graph it is clear that both the quadrilaterls are identical in shape.

In quadrilateral ABCD and quadrilateral WXYZ,

$AB=WX=\sqrt{5}\text{units}$

$DC=ZY=\sqrt{13}\text{units}$

$AD=WZ=\sqrt{5}\text{units}$

$\angle DAC=\angle ZWX$

We know, if any two figures are of the same shape, size, and overlap each other, we can call them as congruent figures.

So, both quadrilaterals ABCD and WXYZ are congruent.

∴ Option (2) is incorrect.