Question

A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A) ABCD is a parallelogram with non-perpendicular adjacent sides. B) ABCD is a trapezoid with only one pair of parallel sides. C) ABCD is a rectangle with non-congruent adjacent sides. D)ABCD is a rhombus with non-perpendicular adjacent sides.

Answer 1

Selection A is appropriate.

Adjacent sides are neither perpendicular nor the same length, but the figure is a parallelogram.

Answer 2

Answer:

(A)

Step-by-step explanation:

It is given that A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5).

Therefore, using the distance formula,

AB=$\sqrt{(0-5)^2+(2-3)^2}=\sqrt{25+1}=\sqrt{26}$,

BC=$\sqrt{(0-0)^2+(7-2)^2}=\sqrt{25}=5$,

CD=$\sqrt{(5-0)^2+(8-7)^2}=\sqrt{25+1}=\sqrt{26}$ and

DA=$\sqrt{(5-5)^2+(8-3)^2}=\sqrt{25}=5$

Now, it can be seen that opposite sides of the quadrilateral are equal but not all the sides are equal, thus the given quadrilateral is not rhombus.

We have to check whether the quadrilateral have perpendicular or non perpendicular adjacent sides.

For this, we take

$AB{\cdot}BC=(-1){\cdot}5+(-5){\cdot}0=-5{\neq}0$

and $AB{\cdot}DA=-1{\cdot}(-5)+(-5)0=5{\neq}0$

The dot products are not equal to zero, then angles A and B are not right. This means that option C is false and option A is correct.