Question

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

(a) Does each triangle have the same starting coordinates? Explain.
(b) Does each triangle have the same ending coordinates? Explain.
(c) Does each triangle have the same change in x-values? Explain.
(d) Does each triangle have the same change in y-values? Explain.
(e) Does each triangle have the same ratio of change in y-values over change in x-values? Explain.

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.....