This page tells you which exercise to open for NCERT Solutions for Class 10 Maths Chapter 7 — Coordinate Geometry — and what method each exercise wants from you. It does not solve the questions; the worked answers live on the Exercise 7.1 and Exercise 7.2 solution pages one level down.
The chapter runs on exactly two tools: the distance formula, drilled in Exercise 7.1 (10 questions), and the section formula, drilled in Exercise 7.2 (10 questions). It builds straight on the coordinate-plane basics from Class 9 — plotting points, abscissa and ordinate. Find your exercise in the directory below, then open its solution page for the steps.
| Exercise | What you get |
|---|---|
| Exercise 7.1 | Solved |
| Exercise 7.2 | Solved |
Exercise 7.1 and Exercise 7.2: what each one tests
Each row below names the exercise, its question count, and the single method it drills. Beneath the table, match the question type in your homework to the exercise that holds it.
What Exercise 7.1 actually asks (10 questions):
- Direct distance between two given points, including the pair that returns to the two towns at (0, 0) and (36, 15) from the chapter opening — pure distance formula, no setup.
- Collinearity by checking that the two smaller distances add to the largest (AB + BC = AC).
- Figure checks: an isosceles triangle, a square read off Fig. 7.8, and naming the quadrilateral a given point set forms.
- Equidistant-point problems — a point on the x-axis, values of x for a given point, and a relation between x and y — each solved by writing AP = BP, squaring, and letting the squared terms cancel into a linear equation.
- One distance-given question that asks for an unknown coordinate; the squaring produces two values.
What Exercise 7.2 actually asks (10 questions):
- Section formula in a directly stated ratio, and the two points of trisection of a segment.
- Finding the ratio from a known dividing point, and the ratio in which the x-axis cuts a segment (set the y-coordinate to zero).
- Mid-point problems in disguise: parallelogram vertices via the mid-points of the diagonals, a circle diameter where the centre is the mid-point of AB, the Sports Day flag question on Fig. 7.12, and a fractional ratio AP = (3/7)AB.
- Dividing a segment into four equal parts.
- One rhombus area question where the distances to compute are the diagonals, not the sides.
The two methods of Chapter 7: distance formula and section formula
The chapter is built on two formulas, both read straight off coordinates. Know these two and which exercise drills each, and you can say what the chapter is for.
The distance formula (Exercise 7.1). Draw a right triangle under the segment joining P(x1, y1) and Q(x2, y2), as in Fig. 7.3 (p. 102). The two legs are (x2 − x1) and (y2 − y1), so Pythagoras gives:
\[ PQ = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \]
Distance is always non-negative, so take only the positive square root. The special case you will use often: the distance of a point P(x, y) from the origin O(0, 0) is \[ OP = \sqrt{x^2 + y^2} \]
The section formula (Exercise 7.2). A point P(x, y) that divides the segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 has coordinates \[ \left( \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2},\; \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right) \]
The formula is derived in section 7.3 (p. 107) by AA similarity from Chapter 6, but you only need to apply it. The special case, ratio 1 : 1, gives the mid-point:
\[ \left( \frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2} \right) \]
Routing rule: a question that asks for a distance, or wants you to name a figure (triangle, square, quadrilateral type), needs the distance formula — Exercise 7.1. A question that gives or asks for a ratio, a dividing point, a mid-point, or a point that splits a segment, needs the section formula — Exercise 7.2.
Common mistakes in Coordinate Geometry Chapter 7
- Swapped weights in the section formula. m1 pairs with the second point’s coordinates and m2 with the first point’s. Mixing them is the classic Exercise 7.2 error (section 7.3, p. 107).
- Incomplete collinearity check. Three points are collinear only if the two smaller distances add to the largest — so compare all three sums, not just any pair. Exercise 7.1 Q3 demands this.
- Negative distances. Distance is never negative; take only the positive square root. When a question gives a distance and asks for an unknown coordinate, the squaring yields two signs, so expect two answers.
- Rhombus sides instead of diagonals. Exercise 7.2 Q10 asks for the area of a rhombus, so the distances to compute are the diagonals, and the area is ½ (product of diagonals) — not the sides.
- Expanding before cancelling. In equidistant-point problems, write AP² = BP² and let the x² and y² terms cancel first (as in Example 4, p. 104). Expanding immediately is slower and error-prone.
How to use this page with the exercise solutions
Find your question in the directory above, note whether it sits in Exercise 7.1 or Exercise 7.2, and open that exercise’s solution page for the worked steps.
Two questions depend on a textbook diagram: Exercise 7.1 Q5 reads the four friends’ seats off Fig. 7.8 (p. 106) and Exercise 7.2 Q3 reads the flag positions off Fig. 7.12 (p. 112) — open the figure before you start rather than guessing coordinates.
For context, the section formula is derived by AA similarity, which you studied in Chapter 6 Triangles, and the coordinate approach flows straight into Chapter 8 Introduction to Trigonometry. Both sit on the Class 10 Maths solutions hub, with the full Class 10 solutions a level up and the complete NCERT solutions list at the top.
To verify the chapter’s two exercises and formulas against the official source, open the NCERT Class 10 Mathematics textbook (Rationalised edition).
| Exercise | What you get |
|---|---|
| Exercise 7.1 | Solved |
| Exercise 7.2 | Solved |
Frequently asked questions
Which exercise of Class 10 Maths Chapter 7 tests the distance formula?
Exercise 7.1 tests the distance formula, and it is the only exercise in the chapter that does. All ten of its questions — direct distances, collinearity, figure checks, and equidistant-point relations — are solved with \[ PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \].
Which exercise tests the section formula and the mid-point formula?
Exercise 7.2 tests the section formula. It also tests the mid-point formula, which is the section formula in its ratio 1 : 1 special case, so several of its questions are mid-point problems in disguise.
How do I tell whether a question needs the distance formula or the section formula?
Ask what the question gives and what it wants. A distance, a figure name, or an equidistance condition means the distance formula. A ratio, a dividing point, a mid-point, or a point that splits a segment wants the section formula.
Is the mid-point formula a special case of the section formula?
Yes. The mid-point divides the segment in the ratio 1 : 1, and substituting m1 = m2 = 1 into the section formula gives \[ \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) \] — the mid-point formula (p. 107).
Which questions in Chapter 7 Coordinate Geometry need a diagram from the textbook?
Two. Exercise 7.1 Q5 needs Fig. 7.8 (p. 106) for the four friends’ seats, and Exercise 7.2 Q3 needs Fig. 7.12 (p. 112) for the flag positions on the school ground. Open the figure before reading the coordinates.
Reference: NCERT textbooks (CBSE).