a We are asked to graph triangles ABC and XYZ on the same coordinate plane. To do so, we are going to plot all the given vertices, and then draw the corresponding triangles. Let's start with the points.
We can now connect them.
b Let's take a look at the graph we created in Part A. We can see that â–³ XYZ is a reflection of â–³ ABC across the vertical line x=1.
If two figures are a reflection of one another, then their corresponding sides are the same length. This suggests that the triangles are congruent. We can set the following conjecture.
Conjecture: △ ABC ≅ △ XYZ
c To prove our conjecture, it is enough to show that the corresponding sides in the triangles are congruent. We can do that using the Distance Formula.
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Let's find the measure of AB by substituting the coordinates of points A and B in the formula.
