A triangle has vertices on a coordinate grid at Q(-8,3)Q(−8,3), R(-8,-9)R(−8,−9), and S(-3,-9).S(−3,−9). What is the length, in units, of QR​?

Answer 1

Hi Anevay M.,

I believe the answer to your question is 12 units. The length, in units, of QR is 12 units.

There are several ways to solve this problem.

Here's one way that will visually show you why the answer is 12 units.

Obtain a sheet of coordinate grid graphing paper. Then plot points Q(-8,3), R(-8,-9), and S(-3,-9) on the paper. Next connect the points with line segments to create your triangle! You should now see a right triangle.

Now look at line segment QR. Notice that line segment QR is partially above and partially below the x-axis. The part of QR that is above the x-axis has a length of 3 units because it runs from the x-axis to positive 3. The part of QR that is below the x-axis has a length of 9 units because it runs from the x-axis to -9. You can now add QR's length above the x-axis (which is 3 units) to QR's length below the x-axis (which is 9 units) to arrive at QR's total length of 12 units. (3 units above the x-axis + 9 units below the x-axis = 12 units total length)

Another way to solve this problem is to notice that the x-coordinates for points Q and R are the same. But the y-coordinates are different! If you know how to subtract integers, you can subtract the y-coordinates from each other (in either order) and take the absolute value of your answer to find the length of QR. So, (-9) - 3 = -12 and the absolute value of -12 is 12. OR 3 - (-9) = 12 and the absolute value of 12 is 12. Subtract in either order and you will find the absolute difference between the y-coordinates is 12 which is the length of QR.

Enjoy exploring math!

Tom W.