Class 10 › Mathematics Coordinate Geometry Class 10 Mathematics · Chapter 7
Practice all → Summary Questions & answers Practise this chapter → View all Page 1 free about 8 min read , Full kit about 55 min read Page 1 free about 8 min read , Full kit about 55 min read View all 12 amazing Marks Booster kits → Coordinate geometry connects algebra with geometry by locating points on a plane using ordered pairs \((x, y)\). The chapter introduces the distance formula to find the length between two points, and the section formula to find the coordinates of a point dividing a line segment in a given ratio (including the midpoint as a special case). These tools let students compute lengths, verify shapes and divide segments without drawing, turning geometric questions into straightforward algebraic calculations.
Distance formula
\(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\).
Section formula
Coordinates of a point dividing a segment in ratio \(m:n\).
Midpoint
The point dividing a segment in the ratio \(1:1\).
Coordinate plane
A plane with x- and y-axes for locating points.
Q1 Write the distance formula between points \((x_1, y_1)\) and \((x_2, y_2)\). Answer Q2 Find the midpoint of the segment joining \((2, 3)\) and \((4, 7)\). Answer Q3 Write the distance formula between points \((x_1, y_1)\) and \((x_2, y_2)\). Answer Q4 Find the distance between the points \((3, 4)\) and \((0, 0)\). Answer Q5 Write the section formula for a point dividing a segment in ratio \(m : n\). Answer Q6 Write the midpoint formula. Answer Q7 Find the midpoint of the segment joining \((2, 3)\) and \((4, 7)\). Answer Q8 How can you check whether three points are collinear using coordinates? Answer Q9 In what ratio does the point \((4, 0)\) divide the segment joining \((1, 0)\) and \((7, 0)\)? Answer Q10 Find the coordinates of the point dividing the join of \((-1, 7)\) and \((4, -3)\) in the ratio \(2 : 3\). Answer Q1 1. (i) Find the distance between the following pair of points : \((2, 3), (4, 1)\) Answer Q2 1. (ii) Find the distance between the following pair of points : \((–5, 7), (–1, 3)\) Answer Q3 1. (iii) Find the distance between the following pair of points : \((a, b), (–a, –b)\) Answer Q4 2. Find the distance between the points \((0, 0)\) and \((36, 15)\). Can you now find the distance between the two towns A and B discussed in Section 7.2. Answer Q5 3. Determine if the points \((1, 5), (2, 3)\) and \((–2, –11)\) are collinear. Answer Q6 4. Check whether \((5, –2), (6, 4)\) and \((7, –2)\) are the vertices of an isosceles triangle. Answer Q7 5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct. Answer Q8 6. (i) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: \((–1, –2), (1, 0), (–1, 2), (–3, 0)\) Answer Q9 6. (ii) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: \((–3, 5), (3, 1), (0, 3), (–1, –4)\) Answer Q10 6. (iii) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: \((4, 5), (7, 6), (4, 3), (1, 2)\) Answer Q11 7. Find the point on the x-axis which is equidistant from \((2, –5)\) and \((–2, 9)\). Answer Q12 8. Find the values of \(y\) for which the distance between the points \(P(2, –3)\) and \(Q(10, y)\) is \(10\) units. Answer Q13 9. If \(Q(0, 1)\) is equidistant from \(P(5, –3)\) and \(R(x, 6)\), find the values of \(x\). Also find the distances \(QR\) and \(PR\). Answer Q14 10. Find a relation between \(x\) and \(y\) such that the point \((x, y)\) is equidistant from the point \((3, 6)\) and \((–3, 4)\). Answer Q1 1. Find the coordinates of the point which divides the join of \((–1, 7)\) and \((4, –3)\) in the ratio \(2 : 3\). Answer Q2 2. Find the coordinates of the points of trisection of the line segment joining \((4, –1)\) and \((–2, –3)\). Answer Q3 3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of \(1\text{m}\) each. \(100\) flower pots have been placed at a distance of \(1\text{m}\) from each other along AD, as shown in Fig. 7.12. Niharika runs \(\frac{1}{4}\)th the distance AD on the 2nd line and posts a green flag. Preet runs \(\frac{1}{5}\)th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? Answer Q4 4. Find the ratio in which the line segment joining the points \((–3, 10)\) and \((6, –8)\) is divided by \((–1, 6)\). Answer Q5 5. Find the ratio in which the line segment joining \(A(1, –5)\) and \(B(–4, 5)\) is divided by the x-axis. Also find the coordinates of the point of division. Answer Q6 6. If \((1, 2), (4, y), (x, 6)\) and \((3, 5)\) are the vertices of a parallelogram taken in order, find \(x\) and \(y\). Answer Q7 7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is \((2, –3)\) and B is \((1, 4)\). Answer Q8 8. If A and B are \((–2, –2)\) and \((2, –4)\), respectively, find the coordinates of P such that \(AP=\frac{3}{7}AB\) and P lies on the line segment AB. Answer Q9 9. Find the coordinates of the points which divide the line segment joining \(A(–2, 2)\) and \(B(2, 8)\) into four equal parts. Answer Q10 10. Find the area of a rhombus if its vertices are \((3, 0), (4, 5), (–1, 4)\) and \((–2, –1)\) taken in order. [Hint : Area of a rhombus = \(\frac{1}{2}\) (product of its diagonals)] Answer
The distance between two points (x₁, y₁) and (x₂, y₂) is:
A √[(x₂−x₁)² + (y₂−y₁)²] B √[(x₂+x₁)² + (y₂+y₁)²] C (x₂−x₁) + (y₂−y₁) D |x₂−x₁| × |y₂−y₁|
Flashcards & interactive practice 
