Question

A quadrilateral is formed by the points A(1,-1), B(0,3), C(5,5), and D(6, 1). Plot the points and use the distance formula to find the lengths of all 4 sides. What type of quadrilateral is this?

Answer 1

If we have the given points on a cartesian point, the result would be:

It is not difficult to see that these points will form a rhombus. In this case, we do expect that the opposite sides have the same size. To verify it, we will use the following formula to calculate the distance among the given points:

`d_(P1-P2)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}`

Substituting each pair, we have:

AB

`\begin{gathered} d_(AB)=\sqrt[]{(1-0)^2+(-1-3)^2}=\sqrt[]{1^2+(-4)^2}=\sqrt[]{1+16}_{} \\ d_(AB)=\sqrt[]{17} \end{gathered}`

BC