NCERT Solutions: Coordinate Geometry (Exercise 7.3)

# NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.3)

Q.1. Find the area of the triangle whose vertices are:
(i) (2, 3), (−1, 0), (2, −4)
(ii) (−5, −1), (3, −5), (5, 2)
Sol. (i) Area of a triangle is given by

Q.2. In each of the following find the value of ‘k’, for which the points are collinear.
(i) (7, −2), (5, 1), (3, k)
(ii) (8, 1), (k, − 4), (2, −5)
Sol. (i) For collinear points, area of triangle formed by them is zero.
Therefore, for points (7, −2) (5, 1), and (3, k), area = 0

(ii) For collinear points, area of triangle formed by them is zero
Therefore, for points (8, 1), (k, −4), and (2, −5), area = 0

Q.3. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, −1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Sol. Let D, E and F are mid-points of the sides AB, BC and AC respectively.

The ratio of ar ΔDEF and ar ΔABC is 1 : 4

Q.4. Find the area of the quadrilateral whose vertices, taken in order, are (−4, −2), (−3, −5), (3, −2) and (2, 3).
Sol. Area of ΔABC

Q.5. You have studied in class IX (Chapter 9, Example 3) that, a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ ABC whose vertices are A (4, −6), B (3, −2) and C (5, 2).
Sol. D is the mid-point of BC, then coordinates of D are

⇒ A median of a triangle divides it into two triangles of equal areas.

The document NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.3) is a part of the Bank Exams Course NCERT Mathematics for Competitive Exams.
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## NCERT Mathematics for Competitive Exams

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## FAQs on NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.3)

 1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes using coordinates. It combines algebraic techniques with geometric concepts to analyze and solve problems related to points, lines, curves, and shapes on a coordinate plane.
 2. How is coordinate geometry used in real life?
Ans. Coordinate geometry finds applications in various fields such as engineering, architecture, navigation, and computer graphics. It is used to design buildings, roads, and bridges, to determine the position of objects in GPS systems, and to create visual effects in movies and video games.
 3. How do you find the distance between two points on a coordinate plane?
Ans. To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, we can use the distance formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2) By substituting the coordinates of the given points into the formula, we can calculate the distance between them.
 4. How do you find the midpoint of a line segment using coordinate geometry?
Ans. To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we can use the midpoint formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2) By substituting the coordinates of the given endpoints into the formula, we can determine the coordinates of the midpoint.
 5. How can we determine if three points are collinear using coordinate geometry?
Ans. Three points (x1, y1), (x2, y2), and (x3, y3) are collinear if the slope of the line passing through any two pairs of points is the same. The slope can be calculated using the formula: Slope = (y2 - y1)/(x2 - x1) If the slopes of all the pairs of points are equal, then the three points are collinear. If the slopes are not equal, then the points are non-collinear.

## NCERT Mathematics for Competitive Exams

276 docs|149 tests

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