# Coordinate Geometry : Exercise - 7.3 (Mathematics NCERT Class 10th)

**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)**Let

and

Area of

**(ii)** Let

and

Area of

= 32 sq. units

**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)**Let the given points be and .

These points lie on a line if

Area

2k = 8

k = 4

Hence, the given points are collinear for k = 4

**(ii)** Let the given points be

If the given points are collinear, then

– 6k = – 18

k = 3

Hence, the given points are collinear for k = 3.

**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

and be the vertices of .

Area

= 1 sq. unit (numerically)

Area

=

sq. units

Let ,i.e., (1, 2), , i.e., (1, 0) and , i.e., (0, 1) are the vertices

of formed by joining the mid-points of the sides of .

Ratio of the area to the area = 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).
**

*Let A(– 4, –2), B (– 3, –5), C (3, –2) and D (2, 3) be the vertices of the quadrilateral ABCD.*

**Sol.**= Area of ABC + Area of ACD

sq. units

**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).
**

*Since AD is the median of , therefore, D is the mid-point of BC. Coordinates of D are*

**Sol.**,i.e., (4, 0).

Area of

= 3sq. units (numerically)

= 3 sq. units (numerically)

Clearly, area = area

Hence, the median of the triangle divides it into two triangles of equal areas.

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