# Class 9 Math Introduction to Coordinate Geometry 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)

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)

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)

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

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)

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)

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)

(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.

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.

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.

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).

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.

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)

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}) .

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.

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| .