The points $H (- 3, 1), I (2, 4)$ , and $J (5, - 1)$ form a triangle. Plot the points then click the "Graph Triangle" 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 characterize the

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Answer

$d_{HJ} = \sqrt{(- 3 - 5)^{2} + (1 - (- 1))^{2}} = \sqrt{64 + 4} = \sqrt{68}$

Steps

Step 1 ： $m_{HI} = \frac{4 - 1}{2 - (- 3)} = \frac{3}{5}$

Step 2 ： $m_{IJ} = \frac{- 1 - 4}{5 - 2} = \frac{- 5}{3}$

Step 3 ： $m_{HJ} = \frac{- 1 - 1}{5 - (- 3)} = - \frac{1}{4}$

Step 4 ： $d_{HI} = \sqrt{(- 3 - 2)^{2} + (1 - 4)^{2}} = \sqrt{25 + 9} = \sqrt{34}$

Step 5 ： $d_{IJ} = \sqrt{(5 - 2)^{2} + (- 1 - 4)^{2}} = \sqrt{9 + 25} = \sqrt{34}$

Step 6 ： $d_{HJ} = \sqrt{(- 3 - 5)^{2} + (1 - (- 1))^{2}} = \sqrt{64 + 4} = \sqrt{68}$