Question

If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find the type of quadrilateral.

Answer 1

Answer:

Regular quadrilateral

Step-by-step explanation:

A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD

We shall use the distance formula to find out the type of quadrilateral

Distance=√{(x1-x2)²+(y1-y2)²}

or (Distance)²=(x1-x2)²+(y1-y2)²

Now AB²=(-4+3)²+(8+4)²=1+144=145

∴AB=√145

BC²=(-3-0)²+(-4+5)²=9+1=10

∴BC=√10

CD²=(0-5)²+(-5-6)²=25+121=146

∴CD=√146

DA²=(5+4)²+(6-8)²=81+4=85

∴DA=√85

Since all the sides are unequal, it is a regular quadrilateral

There is no need to check the length of the diagonals AC and BD as none of the sides are equal. Also, it can be seen that none of the angles can be found out from this information