Find the gradient, equations and intersections of medians, altitudes and perpendicular bisectors using our knowledge of the mid-point as well as parallel and perpendicular lines.

What is the gradient of the straight line through the points \(R(4,0)\) and \(S( - 2,1)\)?

\[\frac{1}{6}\]

\[\frac{2}{3}\]

\[- \frac{1}{6}\]

What is the gradient of the straight line through the points \(A(6,2)\) and \(B(4, - 1)\)?

\[\frac{3}{2}\]

\[\frac{1}{2}\]

Find the midpoint of \(A( - 7,4)\) and \(B(3, - 2)\).

\[( - 2,3)\]

\[( - 2,1)\]

\[( - 5,1)\]

Find the equation of the straight line parallel to \(2y = 3x - 7\) and passing through \((0.5, - 1)\).

\[4y = 6x - 7\]

\[4y = 6x + 7\]

\[2y = 6x - 5\]

Calculate the distance between \(A( - 2, - 3)\) and \(B(3, - 4)\).

\[\sqrt {74}\]

\[\sqrt {26}\]

\[\sqrt {40}\]

A straight line which passes through the points A(-1, 3) and B(k, 4) has a gradient of \(\frac{5}{4}\) What is the value of k?

\[-\frac{1}{5}\]

\[\frac{1}{5}\]

\[\frac{9}{5}\]

What is the gradient of the line with equation \(3y - 7x + 4 = 0\)?

\[- \frac{7}{3}\]

\[\frac{7}{3}\]

\[\frac{3}{7}\]

What is the gradient of the line with equation \(3x + 2y = 5\)?

\[- \frac{2}{3}\]

\[\frac{5}{2}\]

\[- \frac{3}{2}\]

A line perpendicular to the \(x\) axis has an equation in which of the following forms?

\(y = kx\) (\(k\) is a constant)

\(y = k\) (\(k\) is a constant)

\(x = k\) (\(k\) is a constant)

A line with equation \(y = mx + c\) is perpendicular to a line with equation \(y = px + q\) if:

\[p = - \frac{1}{m}\]

\[p = \frac{1}{m}\]

\[p = - m\]