Question

Determine the most specific name for quadrilateral JKLM if the coordinates of thJ(-4,6), K(-1,2), L(1,6), M(4,2)JL ll K.JL is poverticesJ5KM Posverticey=23KMDeter(If slotporal4-3-6-5-22-1037

Answer 1

RHOMBUS

Step-by-step explanation:

Given the quadrilateral JKLM.

With coordinates;

`\begin{gathered} J(-4,6) \\ K(-1,2) \\ L(1,6) \\ M(4,2) \end{gathered}`

Note that;

- If opposite sides are equal and parallel then the shape is a parallelogram.

- If all sides are equal and opposite sides are parallel then the shape is a Rhombus.

From the figure, we can see that the slope of line JL is equal to the slope of line KM.

Also, the slope of the JK is also equal to the slope of line LM.

Therefore, opposite sides of the shape are parallel.

Let us examine the length of each of the sides;

`\begin{gathered} JL=\sqrt[]{(1-(-4))^2+(6-6)^2} \\ JL=\sqrt[]{25} \\ JL=5 \end{gathered}`
`\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{9+16}=\sqrt[]{25} \\ LM=5 \end{gathered}`
`\begin{gathered} KM=\sqrt[]{(4-(-1))^2+(2-2)^2} \\ KM=\sqrt[]{25} \\ KM=5 \end{gathered}`
`\begin{gathered} JK=\sqrt[]{(-1-(-4))^2+(2-6)^2} \\ JK=\sqrt[]{9+16}=\sqrt[]{25} \\ JK=5 \end{gathered}`

So, all the sides of the quadrilateral are equal.

Therefore, since all the sides are equal and opposite sides of the quadrilateral are parallel to each other, then the most specific name for the quadrilateral is RHOMBUS