NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1

Ex 7.1 Class 10 Maths 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:

Ex 7.1 Class 10 Maths Question 2.

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

You can also download the free PDF of Chapter 7 Ex 7.1 Coordinate Geometry NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Ex 7.1 Class 10 Maths Question 3.
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Solution:

Ex 7.1 Class 10 Maths Question 4.
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Solution:

Ex 7.1 Class 10 Maths Question 5.
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the 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:

Ex 7.1 Class 10 Maths 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:

Ex 7.1 Class 10 Maths Question 7.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Solution:

Ex 7.1 Class 10 Maths 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:

Ex 7.1 Class 10 Maths 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:

Ex 7.1 Class 10 Maths 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:

Class 10 Maths Coordinate Geometry Mind Maths

Coordinate of a Point in XY – Plane

The Perpendicular distance of x a point from the y-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate. The x and y taken together in order is called coordinte of point denoted by (x, y).
The coordinate of the points on x-axis are of the form (x, 0) and the points on the y-axis are of the form(0, y). Coordinate of origin is (0, 0).

Sign-conventions in the XY-Plane

The x and y-axis divide the plane into four parts known as quadrants denoted by I, II, III and IV. The sign of x and y-coordinates in each of the quadrant is shown below:

Distance Formula

The distance between any two points
P(x1, y1) and Q(x2, y2) in the plane is given by,

Also the distance of the point P(x1, y1) from the origin is

Section Formula

The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 i.e., 

The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) externally in the ratio, m1 : m2 i.e.,  are

(iii) If the ratio in which P divides AB is K : 1, then the coordinates of the point P will be

Mid-Point Formula

The coordinates of the mid point P of the line segment joining the points A(x1, y1) and B(x2, y2) is

Area of a Triangle

The area of ∆ABC formed by the vertices A(x1, y1), B(x2, y2) is given by

Note:
(i) Area of triangle =  × base × Altitude
(ii) Area of polygon can be calculated by dividing it into the triangular region.
(iii) If three points are collinear then area of the triangle formed by them is zero.

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2

Ex 7.2 Class 10 Maths Question 1.
Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.
Solution:

Ex 7.2 Class 10 Maths Question 2.

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

Ex 7.2 Class 10 Maths 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:

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

Ex 7.2 Class 10 Maths Question 4.
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Solution:

Ex 7.2 Class 10 Maths 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:

Ex 7.2 Class 10 Maths 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:

Ex 7.2 Class 10 Maths 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:

Ex 7.2 Class 10 Maths 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:

Ex 7.2 Class 10 Maths 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:

Ex 7.2 Class 10 Maths 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:

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3

Ex 7.3 Class 10 Maths 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:

Ex 7.3 Class 10 Maths 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:

Ex 7.3 Class 10 Maths 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:

Ex 7.3 Class 10 Maths Question 4.
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).
Solution:

Ex 7.3 Class 10 Maths 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:

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4

Ex 7.4 Class 10 Maths 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).
Solution:

Ex 7.4 Class 10 Maths Question 2.

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

Ex 7.4 Class 10 Maths Question 3.
Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).
Solution:

Ex 7.4 Class 10 Maths Question 4.
The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Solution:

Ex 7.4 Class 10 Maths Question 5.
The class X students school in krishnagar 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 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 ∆PQR, if C is the origin?
Also, calculate the areas of the triangles in these cases. What do you observe?
Solution:

Ex 7.4 Class 10 Maths Question 6.
The vertices of a VABC 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 . calculate the area of the ∆ADe and compare it with the area of ∆ABC.
Solution:

Ex 7.4 Class 10 Maths Question 7.
Let A(4, 2), B(6,5) and C(1, 4) be the vertices of ∆ABC.
(i) The median from A meters BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on the 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 points which are common to all the three medians is called centroid and this point divides each median in the ratio 2: 1]
(v) If A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC, find the coordinates of the centroid of the triangles.
Solution:

Ex 7.4 Class 10 Maths Question 8.
ABCD is a rectangle formed by the 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? a rectangle? or a rhombus? Justify your answer.
Solution:

Coordinate Geometry Class 10 Extra Questions Maths Chapter 7