The distance formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) and the section formula \(\left(\dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2}\right)\). Our own step-by-step solutions to Exercises 7.1 and 7.2, one page per exercise, set out for step marks.
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What it tests. \(PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Use it to test collinearity (the two shorter distances add to the longest), classify triangles and quadrilaterals (compare sides and diagonals) and find equidistant points.
What it tests. The point dividing the join of \((x_1, y_1)\) and \((x_2, y_2)\) internally in the ratio \(m_1 : m_2\) is \(\left(\dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2}\right)\); the midpoint is the case \(1 : 1\). For an unknown ratio, call it \(k : 1\).
Coordinate Geometry has 40 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Coordinate Geometry · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.