26
of [1,2] , [3, 4] & [5, 1) are the
midpoints of the sides of a triangle
then the area of the triangle
i

1 thought on “26<br />of [1,2] , [3, 4] & [5, 1) are the<br />midpoints of the sides of a triangle<br />then the area of the triangle<br />i”

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   Hemant sir 8917668285

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   The mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

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   asked Nov 9, 2017 in Class X Maths by aditya23 (-2,138 points)

   The mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

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   answered Nov 9, 2017 by akansha Expert (2.2k points)

   Let the coordinates of vertices A, B and C of the ∆ABC be (x1, y1), (x2, y2) and (x3, y3) respectively. Let P (3, 4), Q (4, 1) and R (2, 0) be the mid parts of sides BC, AC and AB respectively

   Adding equations (1), (3) and (5)

   2 (x1 + x2 + x3) = 18

   ⇒ x1 + x2 + x3 = 9 … (7)

   Subtracting equation (1), (3) and (5) from equation (7), it is obtained

   x1 = 9 – 6 = 3

   x2 = 9 – 8 = 1

   x3 = 9 – 4 = 5

   Adding equations (2), (4) and (6)

   2 (y1 + y2 + y3) = 10

   ⇒ y1 + y2 + y3 = 5 … (8)

   Subtracting equation (2), (4) and (6) from equation (8), it is obtained

   y1 = 5 – 8 = –3

   y2 = 5 – 2 = 3

   y3 = 5 – 0 = 5

   Thus, the vertices of the triangles are (3, –3), (1, 3) and (5, 5).

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