The points $A$, $B$ and $C$ are vertices of a triangle. The point $A$ is $(-1,3)$ and the

Question

The points $A$, $B$ and $C$ are vertices of a triangle. The point $A$ is $(-1,3)$ and the gradient of the line $AB$ is $2$. Find the equation of the line $AB$. The equation of the line $BC$ is $2x+y=17$. Find the coordinates of $B$. It is given that $\overrightarrow{AE} = \begin{pmatrix} 4 \ 12 \end{pmatrix}$. Find the coordinates of $E$. Given also that $D$ is $(3,7)$, express as a column vector: $\overrightarrow{DE}$. $\overrightarrow{DB}$. What two facts can be deduced about $D$, $E$ and $B$.

Accepted Answer

(a) $y=2x+5$ (b) $B=(3,11)$ (c) $E=(3,15)$ (d)(i) $\begin{pmatrix}0\8\end{pmatrix}$ (ii) $\begin{pmatrix}0\4\end{pmatrix}$ (e) $D,B,E$ are collinear and $B$ is the midpoint of $DE$.

Coordinate Geometry and Vector Applications

Coordinate Geometry and Vector Applications

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