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

This artice brings you the CBSE class 10 Mathematics NCERT Exemplar Problems and Solutions (Part-IV) for chapter 7, Coordinate Geometry. This part consists of Long Answer Type Questions. Each question is provided with a detailed but simple solution. All these questions are very important for CBSE Class 10 Mathematics Board Examination 2017-2018.

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 Δ*ADE.*

**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,} y_{1}), B (x_{2, }*

*y*

_{2}) and

*C*(

*x*

_{3},

*y*

_{3}) are the vertices of Δ

*ABC.*

(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 Δ*ABC?*

**Solution. **

Here, coordinated of the points *A*(*x*_{1}, *y*_{1}), *B*(*x*_{2}, *y*_{2}) and *C*(*x*_{3}, *y*_{3}) are the vertices of Δ*ABC*

are the vertices of Δ*ABC*

(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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