Question

The graph below represents two varying sized triangles plotted in the coordinate plane.

Answer 1

A.  triangle is isosceles in several ways. We will show that |AC|=|BC|. We can use the Pythagorean Theorem to check that these both have length 22+32−−−−−−√. In the calculations below M=(3,1) is the midpoint of AB¯¯¯¯¯¯¯¯.

|AC|2|BC|2=|AM|2+|MC|2=22+32=|BM|2+|MC|2=22+32.

We can also observe that to get from A to C we go over (to the right) by two units and then up three units. To get from B to C we go over (to the left) by two units and then up three units. We travel the same distance to get from A or B to C so A and B are equidistant from C. Finally, we can draw the horizontal line of symmetry for △ABC:

hope this helps.....