Coordinate Geometry, Glossary

Knowing the vocabulary of Coordinate Geometry precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Midpoint, The midpoint of a line segment is the point exactly halfway between its two endpoints. For endpoints $(x_1,y_1)$ and $(x_2,y_2)$, it is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$. It is a special case of dividing a segment in the ratio $1:1$. →
• Gradient, The gradient of a straight line measures its steepness, calculated as the change in $y$ divided by the change in $x$: $m=\frac{y_2-y_1}{x_2-x_1}$. A positive gradient rises from left to right, a negative one falls, and a horizontal line has gradient zero. →
• Division of a Line Segment, Dividing a line segment in the ratio $m:n$ locates the point $P$ that splits the segment from $A$ to $B$ into those proportions. Its coordinates are $\left(\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n}\right)$. This generalises the midpoint formula to any internal ratio. →
• Parallel Lines, Parallel lines never meet and point in the same direction, so they have equal gradients: $m_1=m_2$. In coordinate geometry, showing two lines are parallel usually means proving their gradients are the same. They keep a constant perpendicular distance apart everywhere. →
• Perpendicular Lines, Perpendicular lines meet at a right angle, and the product of their gradients is $-1$, so $m_1 m_2=-1$. This means one gradient is the negative reciprocal of the other. The rule lets us find the equation of a line at right angles to a given line. →
• Area of a Polygon, The area of a polygon with known vertex coordinates is found by the shoelace method, listing the vertices in order and cross-multiplying: for a triangle, area $=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$. The absolute value keeps the area positive regardless of vertex order. →
• Locus, A locus is the path traced by a moving point that obeys a given condition, such as staying a fixed distance from a point, which produces a circle. We translate the condition into an equation in $x$ and $y$ using distance formulas, then simplify to describe the curve. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Coordinate Geometry chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Coordinate Geometry terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Coordinate Geometry questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.