Coordinate Geometry — Six Formulas That Answer Almost Every Question in the Chapter

Coordinate geometry is the chapter where the formula sheet really is the syllabus. Plane geometry asks you to prove things; coordinate geometry asks you to substitute numbers into one of six formulas and arrive at an answer. Nothing has to be constructed and nothing has to be proved.

So the skill being tested is not calculation. It is recognising which formula a question is asking for, from wording that is deliberately varied. 'How far apart', 'the length of the side' and 'the radius' are all the distance formula. 'Divides in the ratio', 'trisects' and 'the point one third of the way along' are all the section formula.

First, the ground rules. A point is written (x, y), always x before y. The plane is cut into four quadrants, numbered anticlockwise from the top right: the first is plus-plus, the second minus-plus, the third minus-minus and the fourth plus-minus. Every point on the x-axis has y = 0, and every point on the y-axis has x = 0.

SSC CGL and CHSL, RRB NTPC, BPSC TRE-4 elementary mathematics and the CTET maths paper all ask from this chapter.

1. What is the distance between the points (3, 4) and (−1, 1)?

2. What is the midpoint of the line segment joining (2, 3) and (8, 7)?

3. Which point divides the line segment joining (1, 2) and (7, 8) internally in the ratio 1 : 2?

4. What is the area of the triangle whose vertices are (0, 0), (4, 0) and (0, 3)?

5. What is the centroid of the triangle with vertices (1, 2), (3, 4) and (5, 0)?

6. What is the slope of the line passing through the points (2, 3) and (4, 7)?

7. If a line is perpendicular to a line of slope 3, what is its slope?

8. In which quadrant does the point (−4, 5) lie?