NCERT Exemplar Solution for CBSE Class 10 Mathematics: Coordinate Geometry (Part-IV)

Here you get the CBSE Class 10 Mathematics chapter 7, Coordinate Geometry: NCERT Exemplar Problems and Solutions (Part-IIIC). This part contains solutions problems included in Exercise 7.3 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Coordinate Geometry. Each solution has been designed to keep it simple and apt.

CBSE Class 10 Mathematics Syllabus 2017-2018

NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Coordinate Geometry:

Exercise 7.4

Long Answer Type Questions:

Question. 1 If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, then find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Solution.                   

Suppose the third vertex of an equilateral triangle be (x, y).

Let A (-4, 3), B (4, 3) and C (x, y).

In equilateral triangle all three sides are equal,

Question. 2 A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, then find the area of ΔADE.

Solution.                   

Here, A (6, 1), B(8, 2) and C (9, 4) are three vertices of a parallelogram ABCD.

Let the fourth vertex of parallelogram be D(x, y).

We know that, the diagonals of a parallelogram bisect each other.                                                              

Question. 3 The points A (x_1, y₁), B (x_2, y₂) and C (x₃, y₃) are the vertices of ΔABC.

(i) The median from A meets BC at D. Find the coordinates of the point D.

(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1

(iii) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 :1 and  CR : RF = 2 : 1

(iv) What are the coordinates of the centroid of the ΔABC?

Solution.

Here, coordinated of the points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are the vertices of ΔABC

are the vertices of ΔABC

(i) As, the median bisect the line segment into two equal parts i.e., here D is the mid-point of BC

(iii) Let the coordinates of a point Q be (p, q)

Question. 4 If the points A (1, -2), B (2, 3), C (a, 2) and D (-4, -3) form a parallelogram, then find the value of a and height of the parallelogram taking AB as base.

Solution.

In parallelogram, we know that diagonals are bisects each other i.e., mid-point of AC = mid-point of BD.

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