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NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry covers the distance formula, section formula, and the formula for the area of a triangle formed by three given points.

Overview of Topics & Subtopics (Click to Jump)

1. Distance Formula

Short Note:

• The distance between two points P(x1, y1) and Q(x2, y2) is PQ = √[(x2−x1)² + (y2−y1)²].

• Distance of a point P(x, y) from the origin O(0,0) is OP = √(x² + y²).

2. Section Formula

Short Note:

• The coordinates of the point P(x, y) which divides the line segment joining A(x1,y1) and B(x2,y2) internally in the ratio m1:m2 are: x = (m1x2+m2x1)/(m1+m2), y = (m1y2+m2y1)/(m1+m2).

• Mid-point Formula (special case with ratio 1:1): Mid-point = [(x1+x2)/2, (y1+y2)/2].

3. Area of a Triangle

Short Note:

• The area of a triangle formed by the points (x1,y1), (x2,y2), (x3,y3) is Area = ½ |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)|.

• If the area of a triangle formed by three points is 0, the points are collinear.

NCERT Textbook Exercise Questions

Find the distance between the points (2, 3) and (4, 1).
Answer: Distance = √[(4−2)² + (1−3)²] = √[4 + 4] = √8 = 2√2 units.
Find the coordinates of the point which divides the line segment joining (4, −3) and (8, 5) in the ratio 3:1 internally.
Answer: x = (3×8 + 1×4)/4 = 28/4 = 7; y = (3×5 + 1×(−3))/4 = 12/4 = 3. So the point is (7, 3).
Find the ratio in which the line segment joining (−3, 10) and (6, −8) is divided by (−1, 6).
Answer: Let the ratio be k:1. Using x-coordinate: −1 = (6k−3)/(k+1) ⇒ −k−1 = 6k−3 ⇒ 7k = 2 ⇒ k = 2/7, so the ratio is 2:7.
Find the area of the triangle whose vertices are (2, 3), (−1, 0) and (2, −4).
Answer: Area = ½ |2(0−(−4)) + (−1)((−4)−3) + 2(3−0)| = ½ |8 + 7 + 6| = ½ × 21 = 10.5 square units.
Find a relation between x and y such that the point (x, y) is equidistant from (3, 6) and (−3, 4).
Answer: Setting distances equal and squaring: (x−3)²+(y−6)² = (x+3)²+(y−4)². Expanding and simplifying gives 3x + y − 5 = 0.
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Class 10 › Mathematics › Coordinate Geometry
Chapter notesRead the chapterPractice MCQsCheck what you rememberChapter test10 questions on one pageOnline testTest 1, 2 and 3, one question at a timePYQPrevious year questionsStudy materialPDF notes
Topics in this chapter: Distance FormulaSection FormulaArea of a Triangle