Problem

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.

Solution

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

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

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

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

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

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

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

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

Step 9 :Answer: Parallelogram

From Solvely APP
Source: https://solvelyapp.com/problems/40704/

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