Coordinate Geometry

On the grid, plot and label the point $D (3, 6)$.

$BC$

______

$AB$.

______

Write down the coordinates of point $A$.

( ______ , ______ )

The coordinates of point $C$ are $(p, -1)$.
The gradient of the line $BC$ is $-2$.

Find the value of $p$.

$p$ = ______

$AB$ and $BC$ are two sides of the parallelogram $ABCD$.

Find the coordinates of point $D$.

( ______ , ______ )

$B$ is the midpoint of the line segment $AC$.

Find the coordinates of $C$.

( ______ , ______ )

The length $AB$ is $\sqrt{t}$.

Find the value of $t$.

$t$ = ______

Find the equation of the line perpendicular to $AB$ that passes through $A$.
Give your answer in the form $y = mx + c$.

$y$ = ______

Find the coordinates of the midpoint of $AB$.

( ______ , ______ )

Find the gradient of the line $AB$.

______

Find the coordinates of the midpoint of the line $PQ$.

( ______ , ______ )

Find the equation of the line perpendicular to $PQ$ which passes through the point $P$.

______

Find the coordinates of the midpoint of $AB$.

( ______ , ______ )

Line $l$ is the locus of points that are equidistant from $A$ and $B$.

Find the equation of line $l$.

______

Find the three inequalities that define the shaded region.

______
______
______

Another region, $R$, is defined by these three inequalities.

Find the area of region $R$.

______ $\text{cm}^2$