Let \(A B C\) be a triangle. Let \(u=\mathbf{A B}\) and \(v=\mathbf{A C}\). If \(D\) is a middle point of…
Let \(A B C\) be a triangle. Let \(u=\mathbf{A B}\) and \(v=\mathbf{A C}\). If \(D\) is a middle point of \(B C\), then \(\mathbf{A D}=\)
\(\frac{u-v}{2}\)
\(\frac{v-u}{2}\)
\(\frac{u+v}{2}\)
\(u+v\)
Solution
If in a \(\triangle A B C, \mathbf{A B}=\mathbf{u}\) and \(\mathbf{A C}=\mathbf{v}\) and \(D\) is mid-point of \(B\) and \(C\), then
\(\mathbf{A D}=\frac{\mathbf{A B}+\mathbf{A C}}{2}=\frac{\mathbf{u}+\mathbf{v}}{2}.\quad \{\text{mid-point formula} \}\)