Question

Which of the following is the area of a quadrilateral with vertices at (-4,2),(1,2),(1,-3) and (-4,-3)

A)20units^2

B)25units^2

C)31units^2

D)36units^2

Answer 1

The correct option is B.

Explanation:

The given vertices are (-4,2),(1,2),(1,-3) and (-4,-3).

Plot these point on a coordinate plate. From the graph it is noticed that the given quadrilateral is a square.

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Use distance formula to find the side length.

`AB=√((1-(-4))^2+(2-2)^2)=√(5^2)=5`

`BC=√((1-1)^2+(-3-2)^2)=√((25)=5`

Since both consecutive sides are equal therefore it is a square.

Area of a square is

`A=a^2`

Where, a is side length.

The side length of the square is 5. So, area of ABCD is

`A=(5)^2`

`A=25`

Therefore the area of quadrilateral is 25 units square. Option B is correct.