The points $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$ are

The line $PQ$ with equation $x - y = 2$ intersects the $x$-axis at $P$. Given $Q$ is $(4, 2)$. Find the equation of the line $PQ$ after it is rotated by $45^{\circ}$ in the counter-clockwise direction about point $P$.

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K=273$ when $F=32$ and that $K=373$ when $F=212$. Express $K$ in terms of $F$ and find the value of $F$,when $K =0$.

Find the equation of the line passing through the point $(1, 2)$ and perpendicular to the line $y = 3x - 1$.

Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is:

The equations of the diagonals of the square formed by the lines $x = 0,$ $y = 0,$ $x = 1,$ and $y = 1$ are