## CBSE Class 10 Maths Solution Chapter 7 Coordinate Geometry PDF

**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)**Solution:**

**Question 2.**

Find the distance between the points (0, 0) and (36, 15).**Solution:**

Let points be A (0, 0) and B (36, 15)

The distance between two points is

**Question 3.**

Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.**Solution:**

Let points be A (1, 5), B (2, 3) and C (-2, -11)

AB + BC ≠ AC

Hence, the given points are not collinear.

**Question 4.**

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

Let points be A(5, -2), B (6, 4) and C (7, -2)

Here, AB = BC

ΔABC is an isosceles triangle.

**Question 5.**

In a classroom, 4 friends are seated at the points A, B, C and D as shown in given figure. 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.**Solution:**

Points A (3, 4), B (6, 7), C (9, 4) and D (6, 1)

Here, AB = BC = CD = DA and AC = BD

ABCD is a square.

Hence, Champa 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)**Solution:**

(i) Let points be A (-1, -2), B (1, 0), C (-1, 2) and D (-3, 0)

Here, AC = BD, AB = BC = CD = AD

Hence, the quadrilateral ABCD is a square.

(ii) Let points be A (-3, 5), B (3, 1), C (0, 3) and D (-1, -4)

The given points do not form any quadrilateral.

(iii) Let points be A(4, 5), B (7, 6), C (4, 3) and D (1, 2)

Here, AB = CD, BC = AD

and AC ≠ BD

The quadrilateral ABCD is a parallelogram.

**Question 7.**

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

Let points be A (2, -5) and B (-2, 9)

Let P (x, 0) be the point on x-axis.

AP = BP

**Question 8.**

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.**Solution:**

Points P (2, -3), Q (10, y) and PQ = 10 units

The distance between two points is

**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.**Solution:**

Points are P (5, -3) and R (x, 6)

Point Q (0, 1) is equidistant from points P (5, -3) and R (x, 6).

**Question 10.**

Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).**Solution:**

Points A(3, 6) and B(-3, 4) are equidistant from point P(x, y)

**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.**Solution:**

**Question 2.**

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).**Solution:**

**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 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given

figure below. Niharika runs th the distance AD on the 2nd line and posts a green flag. Preet runs th 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?**Solution:**

y-coordinate of green flag = x 100 m = 25 m

Coordinates of green flag are P (2, 25)

y-coordinate of red flag = x 100 = 20

Coordinates of red flag are Q (8, 20)

The distance between two points is

The blue flag is in the 5th line, at a distance of 22.5 m.

**Question 4.**

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).**Solution:**

Let the required ratio be k : 1

**Question 5.**

Find the ratio in which 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.**Solution:**

**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.**Solution:**

**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).**Solution:**

**Question 8.**

If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = AB and P lies on the line segment AB.**Solution:**

**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.**Solution:**

**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 = (product of its diagonals)]**Solution:**

**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)**Solution:**

**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)**Solution:**

**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.**Solution:**

**Question 4.**

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

**Question 5.**

You have studied in Class IX, 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).**Solution:**

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