# You have studied in Class IX (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2)

**Solution:**

Let ABC be any triangle whose vertices are A(x_{1}, y_{1}), B(x_{2}, y_{2}), and C(x_{3}, y_{3}).

Area of a triangle = 1/2 (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3 }- y_{1}) + x_{3} (y_{1} - y_{2}))

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

Let M be the mid-point of side BC of ∆ABC.

Therefore, AM is the median in ∆ABC.

Coordinates of point M = ((3 + 5) / 2, (- 2 + 2) / 2) = (4, 0)

Area of a triangle = 1/2 (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3}- y_{1}) + x_{3-}(y_{1} - y_{2}))

By substituting the values of vertices, A, B, M in the formula.

Area of ΔABM = 1/2 [(4){(- 2) - (0)} + (3){(0) - (- 6)} + (4){(- 6)} - (- 2)} square units

= 1/2 (- 8 + 18 - 16) square units

= -3 square units

By substituting the values of vertices, A, M, C in the formula.

Area of ΔAMC = 1/2 [(4){(0) - (-2)} + (4){2 - (- 6)} + (5){(- 6) - (0)}] square units

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

= - 3 square units

However, the area cannot be negative. Therefore, the area of ∆AMC and ∆ABM is 3 square units.

Hence, clearly, median AM has divided ΔABC in two triangles of equal areas.

**Video Solution:**

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

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.3 Question 5:

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

If you have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Therefore for ∆ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2)

Hence, clearly, median AM has divided ΔABC in two triangles of equal areas