Revision sheet

Distance and midpoint

$d = \sqrt{\Delta x^2 + \Delta y^2}$; midpoint = average of the coordinates.

Watch out: average, not half the difference.

Circles

• $(x - h)^2 + (y - k)^2 = r^2$: center $(h, k)$, radius $r$.
• Expanded form: complete the square in $x$ and in $y$.

Watch out: $(x + 3)$ means $h = -3$, and the right side is $r^2$.

Parabolas

• $x^2 = 4py$: focus $(0, p)$, directrix $y = -p$.
• $y^2 = 4px$: focus $(p, 0)$, directrix $x = -p$.

Watch out: divide by 4 to get $p$.

Parallel and perpendicular slopes

Parallel: equal. Perpendicular: $m_1 m_2 = -1$.

Watch out: flip and change the sign.

Equations of lines

$y = y_1 + m(x - x_1)$; find $b$ by substituting the point.

Watch out: parallel lines share the slope, not the intercept.

Partitioning a segment

$A + t(B - A)$; ratio $m : n$ gives $t = \dfrac{m}{m + n}$.

Watch out: count the parts of the ratio.