The points $I (- 6, - 9), J (1, - 3), K (3, 6)$ , and $L (- 4, 0)$ form quadrilateral IJKL. Plot the points then click the "Graph Quadrilateral" button.
Click on the graph to plot a point. Click a point to delete it.
Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.

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Answer

Answer: Parallelogram

Steps

Step 1 ： $m_{I J} = \frac{- 3 - (- 9)}{1 - (- 6)} = \frac{6}{7}$

Step 2 ： $m_{J K} = \frac{6 - (- 3)}{3 - 1} = \frac{9}{2}$

Step 3 ： $m_{K L} = \frac{6 - 0}{3 - (- 4)} = \frac{6}{7}$

Step 4 ： $m_{I L} = \frac{0 - (- 9)}{- 4 - (- 6)} = \frac{9}{2}$

Step 5 ： $d_{I J} = \sqrt{(1 - (- 6))^{2} + (- 3 - (- 9))^{2}} = \sqrt{49 + 36} = \sqrt{85}$

Step 6 ： $d_{J K} = \sqrt{(3 - 1)^{2} + (6 - (- 3))^{2}} = \sqrt{4 + 81} = \sqrt{85}$

Step 7 ： $d_{K L} = \sqrt{((- 4) - 3)^{2} + (0 - 6)^{2}} = \sqrt{49 + 36} = \sqrt{85}$

Step 8 ： $d_{I L} = \sqrt{((- 4) - (- 6))^{2} + (0 - (- 9))^{2}} = \sqrt{4 + 81} = \sqrt{85}$

Step 9 ：Answer: Parallelogram