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Asked: 2021-07-17T14:57:57+05:30 In:

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, – 6), B (3, – 2) and C (5, 2). Q.5

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Google please help me to find the best solution of class 10th exercise 7.3 coordinate geometry. You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, – 6), B (3, – 2) and C (5, 2).

best math solutioncoordinate geometryexercise 7.3 ncertncert class 10th solution
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    1. Guru

      Let the vertices of the triangle be A (4, -6), B (3, -2), and C (5, 2).

      NCERT Solutions for Class 10 Chapter 7-28

      Let D be the mid-point of side BC of ΔABC. Therefore, AD is the median in ΔABC.

      Coordinates of point D = Midpoint of BC = ((3+5)/2, (-2+2)/2) = (4, 0)

      Formula, to find Area of a triangle = 1/2 × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]

      Now, Area of ΔABD = 1/2 [(4) {(-2) – (0)} + 3{(0) – (-6)} + (4) {(-6) – (-2)}]

      = 1/2 (-8 + 18 – 16)

      = -3 square units

      However, area cannot be negative. Therefore, area of ΔABD is 3 square units.

      Area of ΔACD = 1/2 [(4) {0 – (2)} + 4{(2) – (-6)} + (5) {(-6) – (0)}]

      = 1/2 (-8 + 32 – 30) = -3 square units

      However, area cannot be negative. Therefore, the area of ΔACD is 3 square units.

      The area of both sides is the same. Thus, median AD has divided ΔABC in two triangles of equal areas.

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