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Class 9 Math Introduction to Coordinate Geometry 2. Let \mathrm{P} be the point on x -axis with x -coordiante a and \mathrm{Q} be the point on y -axis with y -coordinate b as given below. Find the distance between \mathrm{P} and \math


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2. Let \mathrm{P} be the point on x -axis with x -coordiante a and \mathrm{Q} be the point on y -axis with y -coordinate b as given below. Find the distance between \mathrm{P} and \mathrm{Q} .(iii) a=-8 b=6

2. Show that the points \mathrm{A}(-10) \mathrm{B}(10) and \mathrm{N}(0 \sqrt{3}) are not collinear.
2. Show that the points  \mathrm{A}(-10) \mathrm{B}(10)  and  \mathrm{N}(0 \sqrt{3})  are not collinear.

2. Show that the points \mathrm{A}(-10) \mathrm{B}(10) and \mathrm{N}(0 \sqrt{3}) are not collinear.

3. Find the distance between the following pairs of points.(iii) (00)(-4-3)
3. Find the distance between the following pairs of points.(iii)  (00)(-4-3)

3. Find the distance between the following pairs of points.(iii) (00)(-4-3)

ExampleUsing distance formula show that the points(ii) The above points P Q R and S(1-1) are not collinear.
ExampleUsing distance formula show that the points(ii) The above points  P Q R  and  S(1-1)  are not collinear.

ExampleUsing distance formula show that the points(ii) The above points P Q R and S(1-1) are not collinear.

3. Find the distance between the following pairs of points.(i) (63)(3-3)
3. Find the distance between the following pairs of points.(i)  (63)(3-3)

3. Find the distance between the following pairs of points.(i) (63)(3-3)

1. Find the distance between the following pairs of points.(b) \mathrm{A}(2-6) \mathrm{B}(3-6)
1. Find the distance between the following pairs of points.(b)  \mathrm{A}(2-6) \mathrm{B}(3-6)

1. Find the distance between the following pairs of points.(b) \mathrm{A}(2-6) \mathrm{B}(3-6)

(ii) Distance between the points (10) and (01) is(a). 0(b) 1(c) \sqrt{2} (d) 2
(ii) Distance between the points  (10)  and  (01)  is(a). 0(b) 1(c)  \sqrt{2} (d) 2

(ii) Distance between the points (10) and (01) is(a). 0(b) 1(c) \sqrt{2} (d) 2

9. Show that the points \mathrm{M}(-14) \mathrm{N}(-53) \mathrm{P}(1-3) and \mathrm{Q}(5-2) are the vertices of a parallelogram.
9. Show that the points  \mathrm{M}(-14) \mathrm{N}(-53) \mathrm{P}(1-3)  and  \mathrm{Q}(5-2)  are the vertices of a parallelogram.

9. Show that the points \mathrm{M}(-14) \mathrm{N}(-53) \mathrm{P}(1-3) and \mathrm{Q}(5-2) are the vertices of a parallelogram.

Example 01 Find the mid-point of the line segment joining A(21) and B(34)
Example 01 Find the mid-point of the line segment joining  A(21)  and  B(34)

Example 01 Find the mid-point of the line segment joining A(21) and B(34)

2. Let \mathrm{P} be the point on x -axis with x -coordiante a and \mathrm{Q} be the point on y -axis with y -coordinate b as given below. Find the distance between \mathrm{P} and \mathrm{Q} .(iii) a=-8 b=6
2. Let  \mathrm{P}  be the point on  x -axis with  x -coordiante  a  and  \mathrm{Q}  be the point on  y -axis with  y -coordinate  b  as given below. Find the distance between  \mathrm{P}  and  \mathrm{Q} .(iii)  a=-8 b=6
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2. Let \mathrm{P} be the point on x -axis with x -coordiante a and \mathrm{Q} be the point on y -axis with y -coordinate b as given below. Find the distance between \mathrm{P} and \mathrm{Q} .(iii) a=-8 b=6

Example 1Using the distance formula find the distance between the points.(iv) \mathrm{P}^{\prime}(11) and \mathrm{Q}^{\prime}(22)
Example 1Using the distance formula find the distance between the points.(iv)  \mathrm{P}^{\prime}(11)  and  \mathrm{Q}^{\prime}(22)

Example 1Using the distance formula find the distance between the points.(iv) \mathrm{P}^{\prime}(11) and \mathrm{Q}^{\prime}(22)

1. Using distance formula find the distance between the following pairs of points.(iii) (01) and (23)
1. Using distance formula find the distance between the following pairs of points.(iii)  (01)  and  (23)

1. Using distance formula find the distance between the following pairs of points.(iii) (01) and (23)

1. Find the mid-point of the line segment joining each of the following pairs of points(a) \mathrm{A}(92) \mathrm{B}(72)
1. Find the mid-point of the line segment joining each of the following pairs of points(a)  \mathrm{A}(92) \mathrm{B}(72)

1. Find the mid-point of the line segment joining each of the following pairs of points(a) \mathrm{A}(92) \mathrm{B}(72)

(iii) Mid-point of the points (22) and (00) is(a) (11) (b) (10) (c) 01 ) (d) (-1-1)
(iii) Mid-point of the points  (22)  and  (00)  is(a)  (11) (b)  (10) (c) 01 ) (d)  (-1-1)

(iii) Mid-point of the points (22) and (00) is(a) (11) (b) (10) (c) 01 ) (d) (-1-1)

Example 03 Show that \mathrm{A}(21) \mathrm{B}(51) and \mathrm{C}(26) are the vertices of a right angled triangle.
Example 03 Show that  \mathrm{A}(21) \mathrm{B}(51)  and  \mathrm{C}(26)  are the vertices of a right angled triangle.

Example 03 Show that \mathrm{A}(21) \mathrm{B}(51) and \mathrm{C}(26) are the vertices of a right angled triangle.

4. Whether or not the points \mathrm{A}(23) \mathrm{B}(811) and \mathrm{C}(017) form an isosceles triangle.
4. Whether or not the points  \mathrm{A}(23) \mathrm{B}(811)  and  \mathrm{C}(017)  form an isosceles triangle.

4. Whether or not the points \mathrm{A}(23) \mathrm{B}(811) and \mathrm{C}(017) form an isosceles triangle.

ExampleUsing distance formula show that the points(i) \mathrm{P}(-2-1) \mathrm{Q}(03) and \mathrm{R}(15) are collinear.
ExampleUsing distance formula show that the points(i)  \mathrm{P}(-2-1) \mathrm{Q}(03)  and  \mathrm{R}(15)  are collinear.

ExampleUsing distance formula show that the points(i) \mathrm{P}(-2-1) \mathrm{Q}(03) and \mathrm{R}(15) are collinear.

3. Prove that mid-point of the hypotenuse of a right triangle is equidistant from its three vertices \mathrm{P}(-25) \mathrm{Q}(13) and \mathrm{R}(-10) .
3. Prove that mid-point of the hypotenuse of a right triangle is equidistant from its three vertices  \mathrm{P}(-25) \mathrm{Q}(13)  and  \mathrm{R}(-10) .

3. Prove that mid-point of the hypotenuse of a right triangle is equidistant from its three vertices \mathrm{P}(-25) \mathrm{Q}(13) and \mathrm{R}(-10) .

8. Show that the points A (23) B (811) C (017) and D (-69) are vertices of a square.
8. Show that the points A  (23)  B  (811)  C  (017)  and D  (-69)  are vertices of a square.

8. Show that the points A (23) B (811) C (017) and D (-69) are vertices of a square.

ExampleIf \mathrm{A}(22) \mathrm{B}(2-2) \mathrm{C}(-2-2) and \mathrm{D}(-22) be four non-collinear points in the plane then verify that they form a square A B C D .
ExampleIf  \mathrm{A}(22) \mathrm{B}(2-2) \mathrm{C}(-2-2)  and  \mathrm{D}(-22)  be four non-collinear points in the plane then verify that they form a square  A B C D .
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ExampleIf \mathrm{A}(22) \mathrm{B}(2-2) \mathrm{C}(-2-2) and \mathrm{D}(-22) be four non-collinear points in the plane then verify that they form a square A B C D .

Example 02 Circle with radius 5 unit is drawn with centre C(32) and \mathrm{L}(66) \mathrm{M}(0-1) and \mathrm{N}(-2-3) points are given. Find which of the point is not on the circle. (give reason).
Example 02 Circle with radius 5 unit is drawn with centre  C(32)  and  \mathrm{L}(66) \mathrm{M}(0-1)  and  \mathrm{N}(-2-3)  points are given. Find which of the point is not on the circle. (give reason).
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Example 02 Circle with radius 5 unit is drawn with centre C(32) and \mathrm{L}(66) \mathrm{M}(0-1) and \mathrm{N}(-2-3) points are given. Find which of the point is not on the circle. (give reason).

1. Find the distance between the following pairs of points.(a) \mathrm{A}(92) \mathrm{B}(72)
1. Find the distance between the following pairs of points.(a)  \mathrm{A}(92) \mathrm{B}(72)
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1. Find the distance between the following pairs of points.(a) \mathrm{A}(92) \mathrm{B}(72)

1. Read the following sentences carefully and encircle " \mathrm{T} " in case of True and { }^{\prime} \mathrm{F}^{\prime \prime} in case of False statement.(v) Non-collinear points form a triangle.
1. Read the following sentences carefully and encircle "  \mathrm{T}  " in case of True and  { }^{\prime} \mathrm{F}^{\prime \prime}  in case of False statement.(v) Non-collinear points form a triangle.
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1. Read the following sentences carefully and encircle " \mathrm{T} " in case of True and { }^{\prime} \mathrm{F}^{\prime \prime} in case of False statement.(v) Non-collinear points form a triangle.

5. Do the points A(-12) B(75) and C(2-6) form a right angled triangle.
5. Do the points  A(-12) B(75)  and  C(2-6)  form a right angled triangle.
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5. Do the points A(-12) B(75) and C(2-6) form a right angled triangle.

Example 01 Find the distance between the point P(23) and Q(-45)
Example 01 Find the distance between the point  P(23)  and  Q(-45)
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Example 01 Find the distance between the point P(23) and Q(-45)

ExampleShow that the points \mathrm{A}(-20) \mathrm{B}(-23) \mathrm{C}(23) and \mathrm{D}(20) form a rectangle.
ExampleShow that the points  \mathrm{A}(-20) \mathrm{B}(-23) \mathrm{C}(23)  and  \mathrm{D}(20)  form a rectangle.
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ExampleShow that the points \mathrm{A}(-20) \mathrm{B}(-23) \mathrm{C}(23) and \mathrm{D}(20) form a rectangle.

3. Find the perimeter of the triangle formed by the point \mathrm{A}(00) \mathrm{B}(40) and \mathrm{C}(22 \sqrt{3}) .
3. Find the perimeter of the triangle formed by the point  \mathrm{A}(00) \mathrm{B}(40)  and  \mathrm{C}(22 \sqrt{3}) .
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3. Find the perimeter of the triangle formed by the point \mathrm{A}(00) \mathrm{B}(40) and \mathrm{C}(22 \sqrt{3}) .

5. Show that the diagonals of the parallelogram having vertices \mathrm{A}(12) \mathrm{B}(42) \mathrm{C}(-1-3) and \mathrm{D}(-4-3) bisect each other.
5. Show that the diagonals of the parallelogram having vertices  \mathrm{A}(12) \mathrm{B}(42)   \mathrm{C}(-1-3)  and  \mathrm{D}(-4-3)  bisect each other.
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5. Show that the diagonals of the parallelogram having vertices \mathrm{A}(12) \mathrm{B}(42) \mathrm{C}(-1-3) and \mathrm{D}(-4-3) bisect each other.

Example 1Using the distance formula find the distance between the points.(iii) \mathrm{U}(02) and \mathrm{V}(-30)
Example 1Using the distance formula find the distance between the points.(iii)  \mathrm{U}(02)  and  \mathrm{V}(-30)
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Example 1Using the distance formula find the distance between the points.(iii) \mathrm{U}(02) and \mathrm{V}(-30)

4. If O(00) A(30) and B(35) are three points in the plane find M_{1} and M_{2} as mid-points of the line segments A B and O B respectively. Find \left|M_{1} M_{2}\right| .
4. If  O(00) A(30)  and  B(35)  are three points in the plane find  M_{1}  and  M_{2}  as mid-points of the line segments  A B  and  O B  respectively. Find  \left|M_{1} M_{2}\right| .
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4. If O(00) A(30) and B(35) are three points in the plane find M_{1} and M_{2} as mid-points of the line segments A B and O B respectively. Find \left|M_{1} M_{2}\right| .

MDCAT/ ECAT question bank