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EXERCISE 7.1

**Question 1.** Find the distance between the following pairs of points :

(i) (2, 3), (4, 1)

(ii) (– 5, 7), (– 1, 3)

(iii) (a, b), (– a, – b)

**Question 2.** Find the distance between the points (0, 0) and (36, 15). Can you now find the distance
between the two towns A and B discussed in Section 7.2.

**Question 3.** Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

**Question 4.** Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

**Question 5.** In a classroom, 4 friends are
seated at the points A, B, C and
D as shown in Fig. 7.8. Champa
and Chameli walk into the class
and after observing for a few
minutes Champa asks Chameli,
“Don’t you think ABCD is a
square?” Chameli disagrees.
Using distance formula, find
which of them is correct.

**Question 6.** Name the type of quadrilateral
formed, if any, by the following
points, and give reasons for
your answer:

(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)

(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)

(iii) (4, 5), (7, 6), (4, 3), (1, 2)

**Question 7.** Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

**Question 8.** Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is
10 units

**Question 9.** If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the
distances QR and PR.

**Question 10. **Find a relation between x and y such that the point (x, y) is equidistant from the point
(3, 6) and (– 3, 4).

EXERCISE 7.2

**Question 1.** Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the
ratio 2 : 3.

**Question 2.** Find the coordinates of the points of trisection of the line segment joining (4, –1)
and (–2, –3).

**Question 3.** To conduct Sports Day activities, in
your rectangular shaped school
ground ABCD, lines have been
drawn with chalk powder at a
distance of 1m each. 100 flower pots
have been placed at a distance of 1m
from each other along AD, as shown
in Fig. 7.12. Niharika runs
1
4
th the
distance AD on the 2nd line and
posts a green flag. Preet runs
1
5 th
the distance AD on the eighth line
and posts a red flag. What is the
distance between both the flags? If
Rashmi has to post a blue flag exactly
halfway between the line segment
joining the two flags, where should
she post her flag?

**Question 4.** Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided
by (– 1, 6).

**Question 5.** Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the
x-axis. Also find the coordinates of the point of division.

**Question 6.** If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find
x and y.

**Question 7.** Find the coordinates of a point A, where AB is the diameter of a circle whose centre is
(2, – 3) and B is (1, 4).

**Question 8.** If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that
AP =
3 AB
7 and P lies on the line segment AB.

**Question 9.** Find the coordinates of the points which divide the line segment joining A(– 2, 2) and
B(2, 8) into four equal parts.

**Question 10.** Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in
order. [Hint : Area of a rhombus =
1
2
(product of its diagonals)]

EXERCISE 7.3

**Question 1.** Find the area of the triangle whose vertices are :

(i) (2, 3), (–1, 0), (2, – 4)

(ii) (–5, –1), (3, –5), (5, 2)

**Question 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)

**Question 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.

**Question 4.** Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2), (– 3, – 5),
(3, – 2) and (2, 3).

**Question 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 Δ ABC whose vertices are
A(4, – 6), B(3, –2) and C(5, 2).

EXERCISE 7.4 (Optional)*

**Question 1.** Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the
points A(2, – 2) and B(3, 7).

**Question 2.** Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

**Question 3.** Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).

**Question 4.** The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the
other two vertices.

**Question 5.** The Class X students of a
secondary school in
Krishinagar have been allotted
a rectangular plot of land for
their gardening activity.
Sapling of Gulmohar are
planted on the boundary at a
distance of 1m from each other.
There is a triangular grassy
lawn in the plot as shown in
the Fig. 7.14. The students are
to sow seeds of flowering
plants on the remaining area of
the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?

**Question 6.** The vertices of a Δ ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides
AB and AC at D and E respectively, such that AD AE 1
AB AC 4
= Calculate the area of the
Δ ADE and compare it with the area of Δ ABC. (Recall Theorem 6.2 and Theorem 6.6).

**Question 7. **Let A (4, 2), B(6, 5) and C(1, 4) be 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 do yo observe?

[Note : The point which is common to all the three medians is called the centroid
and this point divides each median in the ratio 2 : 1.]

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- Chapter 1: REAL NUMBERS
**[Ques wise Ans]** - Chapter 2: POLYNOMIALS
**[Ques wise Ans]** - Chapter 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLE
**[Ques wise Ans]** - Chapter 6: Triangles
**[Ques wise Ans]** - Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 11 Constructions
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Chapter 5 Arithmetic Progressions

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