Grade 11 Analytical Geometry

Equations of straight lines through points, parallel and perpendicular lines, and the angle of inclination.

Gr 11 Term 1 - Analytical GeometryTerm 1 - 3 weeks (CAPS)

Practise Analytical Geometry in the app →

What gets asked

• Find the equation of the line through two given points.
• Find a line through a point parallel or perpendicular to a given line.
• Calculate the angle of inclination of a line from its gradient.

You must be able to

• Compute the gradient first; everything else hangs on it.
• Parallel lines share a gradient; perpendicular gradients multiply to $-1$.
• Read the inclination from $\tan \theta =m$, measured anticlockwise from the positive $x$-axis.
• For a negative gradient, the inclination is $180^{\circ }$ minus the reference angle.

Traps that cost marks

• Using the same intercept as the given line when only the gradient should carry over. Parallel copies the gradient only - the new intercept comes from the given point.
• Reporting the calculator's negative angle as the inclination. Inclination lies between 0 and 180 degrees: add the negative answer to 180.
• Taking the reciprocal without changing the sign for a perpendicular gradient. Flip AND negate: a gradient of 2 pairs with negative one half.

Worked example