Triangle XYZ, with vertices X(-1, -3), Y(-1, -1), and Z(-3, -1), is translated 2 units right and one unit down to form triangle X'Yz

Question

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Answer 1

Hi Bob,

This problem was written to give you practice using the x-y coordinate system to plot geometric objects and to understand how to read plots.

The Origin [ the point (0,0) ], the x-axis (positive x to the right) and the y-axis (positive y up) gives us the background orientation.  [Note:  Have you ever noticed in the very famous photo named “Earthrise” that Earth’s North is not UP?]

O.K., when a transposition is performed, the Origin is moved or else the object is moved in relationship to a fixed Origin.

This problem mentions, “Triangle … is translated 2 units right and one unit down.”  This is poor wording, but I’ll assume that the object is moved in relationship to a fixed Origin.

That means that the new x values will be 2 units more than the old x values and the new values of y will be one unit less than the old values of y after triangle is moved.  So, let’s write the new points under the old points so we can be super-accurate:

              X(-1,-3)       Y(-1,-1)       Z(-3,-1)

                  +2  -1          +2  -1          +2  -1

               X'(1,-4)        Y'(1,-2)        Z'(-1,-2)
 
One extra note:  The points in this problem (X,Y,Z,X',Y',Z') are NOT THE SAME as the x and the y axis (and in 3-D Geometry, the Z-axis).  It might have been less confusing to have named them A,B,C,A',B',C',