The points \( \mathrm{H}(-3,1), \mathrm{I}(2,4) \), and \( \mathrm{J}(5,-1) \) 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
Answer
\( \mathrm{d_{HJ}} = \sqrt{(-3-5)^2+(1-(-1))^2} = \sqrt{64+4} = \sqrt{68} \)
Step 1 ：\( \mathrm{m_{HI}} = \frac{4-1}{2-(-3)} = \frac{3}{5} \)
Step 2 ：\( \mathrm{m_{IJ}} = \frac{-1-4}{5-2} = \frac{-5}{3} \)
Step 3 ：\( \mathrm{m_{HJ}} = \frac{-1-1}{5-(-3)} = -\frac{1}{4} \)
Step 4 ：\( \mathrm{d_{HI}} = \sqrt{(-3-2)^2+(1-4)^2} = \sqrt{25+9} = \sqrt{34} \)
Step 5 ：\( \mathrm{d_{IJ}} = \sqrt{(5-2)^2+(-1-4)^2} = \sqrt{9+25} = \sqrt{34} \)
Step 6 ：\( \mathrm{d_{HJ}} = \sqrt{(-3-5)^2+(1-(-1))^2} = \sqrt{64+4} = \sqrt{68} \)
