Question

Plot the points A(0, 3), B(5, 3), C(4, 0) and D(-1, 0) on the graph paper. Identify the figure ABCD then the name of figure​

Answer 1

Solution:

Points given

A(0,3)

B(5,3)

C(4,0)

D(-1,0)

The points are plotted in the attached image.

The figures formed-

A quadrilateral

We will find the distance between the points to get some clues to identify the type of quadrilateral form by the given point.

Now,

Finding the distances

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

AB $= \sqrt{25 + 0}$

AB $= 5$

So,

AB is 5 units

Now

CD $= \sqrt{ {(4 + 1)}^{2} + {(0 - 0)}^{2} }$

CD $= \sqrt{25}$

CD $= 5$

Now,

BC $= \sqrt{ {(4 - 5)}^{2} + {(0 - 3)}^{2} }$

BC $= \sqrt{ {( - 1)}^{2} + {( - 3)}^{2} }$

BC $= \sqrt{1 + 9}$

BC $= \sqrt{10}$

So,

BC = √10 units

And

AD $= \sqrt{ {( - 1 - 0)}^{2} + {(0 - 3)}^{2} }$

AD $= \sqrt{ {( - 1)}^{2} + {( - 3)}^{2} }$

AD $= \sqrt{1 + 9}$

AD $= \sqrt{10}$

AD is also √10 units

We got

AB = DC

And

BC = AD

So its opposite sides are equal so the quadrilateral is a parallelogram.