Question

What is the most precise name for quadrilateral ABCD with vertices A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4)?

A) quadrilateral

B) parallelogram

C) rhombus

D) rectangle

Answer 1

D a rectangle because it has four sides easy for abcd

Answer 2

Option D.

Explanation:

The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula, we get

`AB=√(\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2)=√(0^2+(2)^2)=√(4)=2`

Similarly,

`BC=√(\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2)=3`

`CD=√(\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2)=2`

`AD=√(\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2)=3`

`AB = CD`

`BC = AD`

Measure of diagonals:

`AC=√(\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2)=√(13)`

`BD=√(\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2)=√(13)`

`AC = BD`

Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.

Hence, the correct option is D.