Barycentric coordinates/Point representation/Exercise/Solution
< Barycentric coordinates < Point representation <
Exercise
We have
P
+
P
P
→
=
P
+
0
=
P
.
{\displaystyle {}P+{\overrightarrow {PP}}=P+0=P\,.}
We have
P
+
P
P
→
+
P
Q
→
−
P
Q
→
=
P
+
0
=
P
.
{\displaystyle {}P+{\overrightarrow {PP}}+{\overrightarrow {PQ}}-{\overrightarrow {PQ}}=P+0=P\,.}
We have
P
+
P
,
P
+
v
→
−
P
,
Q
+
v
→
+
P
Q
→
=
P
+
v
+
Q
+
v
,
P
→
+
P
Q
→
=
P
+
v
+
Q
+
v
,
Q
→
=
P
+
v
−
v
=
P
.
{\displaystyle {}{\begin{aligned}P+{\overrightarrow {P,P+v}}-{\overrightarrow {P,Q+v}}+{\overrightarrow {PQ}}&=P+v+{\overrightarrow {Q+v,P}}+{\overrightarrow {PQ}}\\&=P+v+{\overrightarrow {Q+v,Q}}\\&=P+v-v\\&=P.\end{aligned}}}
To the exercise
