The vertices of ∆ ABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.
Let three vertices be A (−2, 1) and B (5, 4) and C(2, −3)
Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)
= 
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|
Area of ∆ABC
= 
|-2(4 – (-3)) + 5(-3 -1) + 2(1 – 4)|
= 
|-14 - 20 - 6|
= 20 sq. units
Now to find length of BC,
By distance formula,
XY = 
For BC,
BC = 
= 
= 
sq. units
Area of ∆ABC = 
× Base × Altitude
∴ 20 = 
× 
× Altitude
∴ Altitude = 
units
Hence, the length of altitude through A is 
units.
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