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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Find Th Co-ordinates of the Midpoint of the Line Segment Joining P(0, 6) and Q(12, 20). - Geometry Mathematics 2

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प्रश्न

Find th co-ordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).

उत्तर

P(0, 6)          Q(12, 20)

   ↓                      ↓
(x1, y1)           (x2, y2)
Let co-ordinates of midpoint be (x, y)
By formula for midpoint.,
`x =( x_1+ x_2)/2`
= `(0+12)/2`
= `12/2   = 6`

 

y = `(y_1+y_2)/2`
y = `(6+20)/2`
= `26/2`
= 13
∴ PQ co-ordinates of midpoint of segment PQ are(6, 13)

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The Mid-point of a Line Segment (Mid-point Formula)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Balbharati Model Question Paper Set 3

संबंधित प्रश्‍न

Points A(–5, x), B(y, 7) and C(1, –3) are collinear (i.e. lie on the same straight line) such that AB = BC. Calculate the values of x and y.


Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).


Find the coordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).


Find the midpoint of the line segment joining the following pair of point : 

(a+b, b-a) and (a-b, a+b) 


Find the length of the median through the vertex A of triangle ABC whose vertices are A (7, -3), B(S, 3) and C(3, -1).


A , B and C are collinear points such that AB = `1/2` AC . If the coordinates of A, B and C are (-4 , -4) , (-2 , b) anf (a , 2),Find the values of a and b.


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show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.


The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex.


The mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle


The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square


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The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is


Find the co-ordinates of centroid of a triangle if points D(–7, 6), E(8, 5) and F(2, –2) are the mid-points of the sides of that triangle.


Find the coordinates of the mid-point of the line segment with points A(– 2, 4) and B(–6, –6) on both ends.


Point P is the centre of the circle and AB is a diameter. Find the coordinates of points B if coordinates of point A and P are (2, – 3) and (– 2, 0) respectively.


Given: A`square` and P`square`. Let B (x, y)

The centre of the circle is the midpoint of the diameter.

∴ Mid point formula,

`square = (square + x)/square`

⇒ `square = square` + x

⇒ x = `square - square`

⇒ x = – 6

and `square = (square + y)/2`

⇒ `square` + y = 0

⇒ y = 3

Hence coordinates of B is (– 6, 3).


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