Class |
10 |

Chapter |
Coordinate Geometry |

Subject |
Math |

Category |
Important Question Answer |

**Class 10 Math Chapter 7 Important Question Answer**

**Q1. Find the distance between the points (-5, 7) and (-1, 3). Most Important**

**Ans**. Distance between the points =

=

= =

**Q2. Find the ratio in which the line joining (3, 4) and (-4, 7) is divided by y- axis. Also find the coordinates of the point of intersection. Most Important**

**Ans**. Let the ratio be k : 1. Then by the section formula, the coordinates of the point which divides AB in the ratio k : 1 are

The point lies on the y-axis, and we know that on the y-axis the x-coordinate is 0.

Therefore, = 0

-4k + 3 = 0

k =

Therefore, ratio is 3:4. Putting the value of k = , we get the point of intersection

**Q3. Find the distance between points (a, b) and (-a, -b).**

**Ans**. The distance between the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by

Therefore,

The distance between the points = = =

**Q4. If (3, 4) is mid point of the line segment whose one end is (7, -2), then find the coordinates of the other end point.**

**Ans**. The mid-point of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are

We have given mid points (3, 4) and coordinates of one point (7, -2) i.e ((x_{1}, y_{1}) and we have to find (x_{2}, y_{2}).

On comparing,

3 =

3 =

x_{2} = -1

Similarly, -2 =

-2 =

y_{2 }= -2

Therefore, the required coordinates of other end are (-1, -2)

**Q5. Find the mid point of the line segment whose end points are (4, 5) and (2, -1).**

**Ans**. The mid-point of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are

Therefore, the mid point of line segment **(**4, 5) and (2, -1) are

=

= (3, 2)

**Q6. Find the mid point of the line joining the points (4, 7) and (2, 3).**

**Ans**. The mid-point of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are

Therefore, the mid point of line segment **(**4, 7) and (2, 3) are

=

= (3, 5)

**Q7. If origin is at one end of a line segment whose mid point is (1, 0), find the coordinates of other end of segment.**

**Ans**. The mid-point of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are

We have given mid points (1, 0) and coordinates of one point at origin means (0, 0) i.e ((x_{1}, y_{1}) and we have to find (x_{2}, y_{2}).

On comparing,

1 =

Putting value of x_{1 }in equation we get,

1 =

x_{2} = 2

Similarly, 0 =

Putting value of y_{1} in equation,

0 =

y_{2 }= 0

Therefore, the required coordinates of other end are (2, 0)

**Q8. Find the co-ordinates of a point A where AB is the diameter of a circle whose centre is (2, -3) and co-ordinates of B is (1, 4).**

**Ans**. The mid-point of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are

We have given mid points (2, -3) and coordinates B is (1, 4) and we have to find coordinates of A (x_{1}, y_{1}).

On comparing,

2 =

4 =

x_{1} = 3

Similarly, -3 =

-6 =

Y_{1 }= -10

Therefore, the required coordinates of A are (3, -10)

**Q9. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.**

Ans. We know that diagonals of a parallelogram bisect each other.

So, the coordinates of the mid point of AC = coordinates of the mid-point of BD

i.e.

so,

p = 7

**Q10. Find the ratio in which the y-axis divides the line segment joining the points (5, 6) and (-1, -4). Also find the point of intersection.**

**Ans**. Let the ratio be k : 1. Then by the section formula, the coordinates of the point which divides AB in the ration k : 1 are

This point lies on the y-axis, and we know that on the y-axis the x-coordinate is 0.

Therefore, = 0

-k + 5 = 0

k = 5

Therefore ratio is 5:4. Putting the value of k=5, we get the point of intersection are .

**Q11. Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by **** (-1, 6).**

**Ans**. Let the ratio k : 1. Using section formula, we get

(-1, 6) =

So, -1 =

-k – 1 = 6k – 3

7k = 2

k =

i.e. k : 1 = 2 : 7

So, the point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7.

**Q12. Find the co-ordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).**

**Ans**. Let P and Q be the points of trisection of AB.

i.e. AP=PQ=QB

Therefore, P divides AB internally in the ratio 1 : 2. Therefore, the coordinates of P, by applying the section formula, are

, i.e. (-1, 0)

Now, Q also divides AB internally 2:1. So, the coordiates of Q are

, i.e., (-4, 2)

**Q13. In what ratio does the point (-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8).**

**Ans**. Let the ratio k : 1. Let (-4, 6) divide AB internally in the ratio k : 1. Using the section formula, we get

(-4, 6) =

So, -4 =

-4k – 4 = 3k – 6

7k = 2

k =

i.e k : 1 = 2 : 7

So, the point (-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8) in the ratio 2 : 7.

**[Note : You can check for the y-coordinate also.]**

**Q14. Find the coordinates of the point which divide the line segment joining the points (4, -3) and (8, 5) in a ratio 3 : 1 internally. Most Important**

Ans. Let P(x, y) be the required point. Using the section formula, we get

Therefore, (7, 3) is the required point.

Also Read |
Class 10 Math NCERT Solution |

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Class 10 Important Questions [Latest] |