# You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two

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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).

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AD Median is drawn to side BC which is the vertex of ∆ABC.

Median AD divides AABC into two triangles ∆ABD and ∆ADC which are equal in area.

∴ BD = DC.

(i) As per Mid-Points formula,

Coordinates of D are

$\sqrt{(4)^2 - (0)^2}$

$\sqrt{16, 0}$

= (4,0)

∴ Coordinates of D are (4, 0)

(ii) Now, Area of ∆ABD:

= – 3 sq. units.

∴ Area of ∆ADC = -3 sq. units.

∴ Area of ∆ABC : = Area of ∆ABD + Area of ∆ADC

= (-3) +(-3)

= -6 sq. units.

(iv) Now, Area of ∆ABC : (Direct Method)