Karen Morrison and Nick Hamshaw Solutions for Exercise 5: Exercise 10.5

Show that the line through the points $A\left(6,0\right)$ and $B\left(0,12\right)$ is perpendicular to the line through $P\left(8,10\right)$ and $Q\left(4,8\right)$.

Show that the line through the points $A\left(6,0\right)$ and $B\left(0,12\right)$ is perpendicular to the line through $M(-4,-8)$ and $N\left(-1,-\frac{13}{2}\right)$.

Given, $A\left(0,0\right)$ and $B\left(1,3\right)$. Find the equation of the line perpendicular to $AB$ with a $y‐$intercept of $5$.

Find the equation of a line perpendicular to $2x-y-1=0$ and passing through $\left(2,-\frac{1}{2}\right)$.

Find the equation of a line perpendicular to $2x+2y=5$ and passing through $\left(1,-2\right)$.

Line $A$ joins the points $\left(6,0\right)$ and $\left(0,12\right)$. Line $B$ joins the points $\left(8,10\right)$ and $\left(4,8\right)$. Determine the gradient of each line and state whether $A$ is perpendicular to $B$.

Line $MN$ joins points $\left(7,4\right)$ and $\left(2,5\right)$. Find the equation of $AB$, perpendicular bisector of $MN$.

Show that points $A\left(-3,6\right), B\left(-12,-4\right)$ and $C\left(8,-5\right)$ could not be the vertices of a rectangle $ABCD$.