CLASS – X Mathematics

Chapter-07 Coordinate Geometry

(Exercise 7.1)

Questions:

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)

2. Find the distance between the points (0, 0) and (36, 15).Also, find the distance

between towns A and B if town B is located at 36 km east and15 km north of town A.

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

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

5. In a classroom, 4 friends are seated at the

points A (3, 4), B (6, 7), C (9, 4) and D (6,

1). 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.

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)

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

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

10 units.

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.

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)

Questions:

1. Find the coordinates of the point which divides the join of(–1, 7) and (4, –3) in the

ratio 2:3.

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

(–2, –3).

3. To conduct sports day activities, in your

rectangular shaped school ground ABCD, lines

have been drawn with chalk powder at a distance

of 1 m each. 100 flower pots have been placed at a

distance of 1 m from each other along AD. Niharika

runs 14th of the distance AD on the 2nd line and

posts a green flag. Preet runs 15th of 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?

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

divided by (–1, 6).

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.

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

and y.

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).

8. If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that AP

=

7

3

AB and P lies on the line segment AB.

9. Find the coordinates of the points which divides the line segment joining A (–2, 2) and

B (2, 8) into four equal parts.

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 = ½ (product of its diagonals)}

(Exercise 7.3)

Questions:

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

(i) (2, 3), (–1, 0), (2, –4)

(ii) (–5, –1), (3, –5), (5, 2)

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)

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.

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

(3, –2) and (2, 3).

5. We know that 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).

(Exercise 7.4)

Questions:

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).

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

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

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

other two vertices.

5. The class X students of a secondary school in

Krishinagar have been allotted a rectangular

plot of land for their gardening activity. Saplings

of Gulmohar are planted on the boundary at a

distance of 1 m from each other. There is a

triangular grassy lawn in the plot as shown in

the figure. 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 D PQR if C is the origin? Also

calculate the area of the triangle in these cases. What do you observe?

6. The vertices of a D 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 D ADE and compare it with the area of D ABC.

7. Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of D 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 you observe?

(Note: The point which is common to all the three medians is called centroid and

this point divides each median in the ratio 2 : 1)

(v) If A( ) 1 1 x , y , B( ) 2 2 x , y and C( ) 3 3 x , y are the vertices of D ABC, find the coordinates

of the centroid of the triangle.

8. ABCD is a rectangle formed by joining points A(-1,-1), B(-1,4), C(5,4) and D(5,-1).

P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral

PQRS a square? Or a rhombus? Justify your answer.