Question

1. is triangle wxy congruent to triangle jkl? if so, what transformation(s) map triangle wxy onto triangle jkl? if not, how do you know that they are are not congruent? triangle wxy is congruent to triangle jkl

Explanation:

Step1: Identify side - lengths

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the side - lengths of both triangles. For example, if $W(x_1,y_1)$ and $X(x_2,y_2)$ in $\triangle WXY$, then $WX=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Do this for all sides of $\triangle WXY$ and $\triangle JKL$.

Step2: Check congruence

If the corresponding side - lengths of $\triangle WXY$ and $\triangle JKL$ are equal (i.e., $WX = JK$, $XY=KL$, $WY = JL$), then the triangles are congruent.

Step3: Find transformation

If congruent, observe the orientation and position of the two triangles. If the orientation is the same, it may be a translation. If the orientation is different, it could be a rotation followed by a translation. For example, if we can find a point $P$ such that rotating $\triangle WXY$ around $P$ by a certain angle and then translating it gives $\triangle JKL$, we have found the transformation.

Answer:

We need to calculate side - lengths using the distance formula to confirm congruence. If congruent, transformation can be found by observing position and orientation. Without specific coordinates, we cannot give a definite answer on congruence and transformation.