Pls help me on 21 , 22 , and 23

9514 1404 393

  21.  perpendicular

  22.  neither

  23.  parallel

Step-by-step explanation:

It can help to plot the points on a graph and draw lines through them. This can also let you count grid squares, which can make it easier to find the slope.

21. See attachment 1. The lines are perpendicular.

QR has a slope of -3/2. ST has a slope of 2/3, the opposite reciprocal.

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22. See attachment 2. The lines are neither parallel nor perpendicular.

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23. The x-coordinates of Q and R are the same, so this is a vertical line at x=-1. The x-coordinates of S and T are also the same, so it is a vertical line at x=11. The two vertical lines are parallel to each other.

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Additional comment

When you have a number of problems that all require similar arithmetic, it can be useful to embed that arithmetic in a spreadsheet. You have to enter the numbers somewhere to "show work" or perform a calculation, so you may as well enter them into a spreadsheet that does the calculation for you.

Of course, the slope formula is ...

  m = (y2 -y1)/(x2 -x1)

If you simply show the values of m for each pair of points, you can see if they are equal (lines are parallel). You can also have the spreadsheet compute their product to see if it is -1 (lines are perpendicular). If you get a #DIV/0! error, it means the line is vertical (and the product will also give an error). You can avoid error messages by making the spreadsheet more sophisticated, but that isn't necessary for the purpose here.

1/4 because there is 4 grades.