In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 7 Coordinate Geometry Ex 7.2. These solutions are based on new NCERT Syllabus.

## NCERT Class 10th Maths Solutions Chapter 7 Coordinate Geometry Ex 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:

Let the required point be P(x, y).

Here the end points are (-1, 7) and (4, – 3)

Ratio = 2 : 3 = m_{1} : m_{2}

∴ x = \(\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}\)

= \(\frac{(2 \times 4)+3 \times(-1)}{2+3}=\frac{8-3}{5}=\frac{5}{5}=1\)

And y = \(\frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}\)

= \(\frac{2 \times(-3)+(3 \times 7)}{2+3}=\frac{-6+21}{5}=\frac{15}{5}=3\)

Thus, the required point is (1, 3)

Question 2.

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

Solution:

Let the given points be A(4, -1) and B(-2, -3)

Let the points P and Q trisects AB.

i.e., AP = PQ = QB

i.e., P divides AB in the ratio of 1 : 2 and Q divides AB in the ratio of 2 : 1

Let the coordinates of P be (x, y)

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 the figure. 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 ?.

Solution:

Let us consider ‘A’ as origin, then

AB is the x-axis.

AD is the y-axis.

Now, the position of green flag-post is (2, \(\frac{100}{4}\)) or (2, 25)

And the position of the red flag-post is (8, \(\frac{100}{5}\)) or (8, 20)

Distance between both the flags

Let the mid-point of the line segment joining the two flags be M(x, y).

or x = 5 and y = 22.5

Thus, the blue flag is on the 5th line at a distance 22-5 m above AB.

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 given points are A(-3, 10) and B(6, -8).

Let the point P(-1, 6) divides AB in the ratio m_{1} : m_{2}.

∴ Using the section formula, we have

⇒ -1(m_{1} + m_{2}) = 6m_{1} – 3m_{2}

and 6(m_{1} + m_{2}) = – 8m_{1} + 10m_{2}

⇒ -m_{1} – m_{2} – 6m_{1} + 3m_{2} = 0

and 6m_{1} + 6m_{2} + 8m_{1} – 10m_{2} = 0

⇒ -7m_{1} + 2m_{2} = 0 and 14m_{1} – 4m_{2} = 0 or 7m_{1} – 1m_{2} = 0

⇒ \(\frac{m_{1}}{m_{2}}=\frac{2}{7}\) and \(\frac{m_{1}}{m_{2}}=\frac{2}{7}\)

⇒ 2m_{2} = 7m_{1} and 7m_{1} = 2m_{2}

⇒ m_{1 }: m_{2} = 2 : 7 and m_{1} : m_{2} = 2 : 7

Thus, the required ratio is 2 : 7.

Question 5.

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

Solution:

The given points are A( 1, -5) and B(-4, 5). Let the required ratio = k:l and the required point be P(x, y).

Since the point P lies on x-axis,

∴ Its y-coordinate is 0.

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:

Let the given points are A( 1, 2), B(4, y), C(x, 6) and D(3, 5)

Since, the diagonals of a parallelogram bisect each other.

∴ The coordinates of P are :

∴ The required values of x and y are 6 and 3 respectively.

Question 7.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and Bis (1,4).

Solution:

Let centre of the circle is 0(2, -3) and the end points of the diameter be A(x, y) and B(1, 4)

Since, the centre of a circle bisects the diameter.

∴ 2 = \(\frac{x+1}{2}\) ⇒ x + 1 = 4 or x = 3

And -3 = \(\frac{y+4}{2}\) ⇒ y + 4 = -6 or y = -10

Thus, the coordinates of A are (3, -10)

Question 8.

If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = \(\frac{3}{7}\) AB and Plies on the line segment AB.

Solution:

Here, the given points are A(-2, -2) and B(2, -4)

Let the coordinates of P are (x, y)

Since, the point P divides AB such that

AP = \(\frac{3}{7}\)AB or \(\frac{A P}{A B}\) = \(\frac{3}{7}\)

⇒ AB = AP + BP

⇒ \(\frac{A P+B P}{A P}\) = \(\frac{7}{3}\)

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:

Here, the given points are A(-2, 2) and B(2, 8)

Let P_{1}, P_{2} and P_{3} divide AB in 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 = \(\frac{1}{2}\) (product of its diagonals)]

Solution:

Let the vertices of the given rhombus are A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1)

In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 7 Coordinate Geometry Ex 7.2. These solutions are based on new NCERT Syllabus.

## NCERT Class 10th Maths Solutions Chapter 7 Coordinate Geometry Ex 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:

Let the required point be P(x, y).

Here the end points are (-1, 7) and (4, – 3)

Ratio = 2 : 3 = m_{1} : m_{2}

∴ x = \(\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}\)

= \(\frac{(2 \times 4)+3 \times(-1)}{2+3}=\frac{8-3}{5}=\frac{5}{5}=1\)

And y = \(\frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}\)

= \(\frac{2 \times(-3)+(3 \times 7)}{2+3}=\frac{-6+21}{5}=\frac{15}{5}=3\)

Thus, the required point is (1, 3)

Question 2.

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

Solution:

Let the given points be A(4, -1) and B(-2, -3)

Let the points P and Q trisects AB.

i.e., AP = PQ = QB

i.e., P divides AB in the ratio of 1 : 2 and Q divides AB in the ratio of 2 : 1

Let the coordinates of P be (x, y)

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 the figure. 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 ?.

Solution:

Let us consider ‘A’ as origin, then

AB is the x-axis.

AD is the y-axis.

Now, the position of green flag-post is (2, \(\frac{100}{4}\)) or (2, 25)

And the position of the red flag-post is (8, \(\frac{100}{5}\)) or (8, 20)

Distance between both the flags

Let the mid-point of the line segment joining the two flags be M(x, y).

or x = 5 and y = 22.5

Thus, the blue flag is on the 5th line at a distance 22-5 m above AB.

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 given points are A(-3, 10) and B(6, -8).

Let the point P(-1, 6) divides AB in the ratio m_{1} : m_{2}.

∴ Using the section formula, we have

⇒ -1(m_{1} + m_{2}) = 6m_{1} – 3m_{2}

and 6(m_{1} + m_{2}) = – 8m_{1} + 10m_{2}

⇒ -m_{1} – m_{2} – 6m_{1} + 3m_{2} = 0

and 6m_{1} + 6m_{2} + 8m_{1} – 10m_{2} = 0

⇒ -7m_{1} + 2m_{2} = 0 and 14m_{1} – 4m_{2} = 0 or 7m_{1} – 1m_{2} = 0

⇒ \(\frac{m_{1}}{m_{2}}=\frac{2}{7}\) and \(\frac{m_{1}}{m_{2}}=\frac{2}{7}\)

⇒ 2m_{2} = 7m_{1} and 7m_{1} = 2m_{2}

⇒ m_{1 }: m_{2} = 2 : 7 and m_{1} : m_{2} = 2 : 7

Thus, the required ratio is 2 : 7.

Question 5.

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

Solution:

The given points are A( 1, -5) and B(-4, 5). Let the required ratio = k:l and the required point be P(x, y).

Since the point P lies on x-axis,

∴ Its y-coordinate is 0.

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:

Let the given points are A( 1, 2), B(4, y), C(x, 6) and D(3, 5)

Since, the diagonals of a parallelogram bisect each other.

∴ The coordinates of P are :

∴ The required values of x and y are 6 and 3 respectively.

Question 7.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and Bis (1,4).

Solution:

Let centre of the circle is 0(2, -3) and the end points of the diameter be A(x, y) and B(1, 4)

Since, the centre of a circle bisects the diameter.

∴ 2 = \(\frac{x+1}{2}\) ⇒ x + 1 = 4 or x = 3

And -3 = \(\frac{y+4}{2}\) ⇒ y + 4 = -6 or y = -10

Thus, the coordinates of A are (3, -10)

Question 8.

If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = \(\frac{3}{7}\) AB and Plies on the line segment AB.

Solution:

Here, the given points are A(-2, -2) and B(2, -4)

Let the coordinates of P are (x, y)

Since, the point P divides AB such that

AP = \(\frac{3}{7}\)AB or \(\frac{A P}{A B}\) = \(\frac{3}{7}\)

⇒ AB = AP + BP

⇒ \(\frac{A P+B P}{A P}\) = \(\frac{7}{3}\)

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:

Here, the given points are A(-2, 2) and B(2, 8)

Let P_{1}, P_{2} and P_{3} divide AB in 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 = \(\frac{1}{2}\) (product of its diagonals)]

Solution:

Let the vertices of the given rhombus are A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1)