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What is the formula for the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3)?

Class 10Area of a Triangle (Coordinates)Geometry — Coordinates

A $\frac{1}{2} ∣ x 1 (y 2 - y 3) + x 2 (y 3 - y 1) + x 3 (y 1 - y 2) ∣$
B $\frac{1}{2} ∣ x 1 (y 2 + y 3) + x 2 (y 3 + y 1) + x 3 (y 1 + y 2) ∣$
C|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
D $\frac{1}{2} ∣ x 1 + x 2 + x 3 - y 1 - y 2 - y 3∣$

Step-by-Step Solution

The standard coordinate area formula is Area =

\frac{1}{2} ∣ x 1 (y 2 - y 3) + x 2 (y 3 - y 1) + x 3 (y 1 - y 2) ∣

.

Answer: A)

\frac{1}{2} ∣ x 1 (y 2 - y 3) + x 2 (y 3 - y 1) + x 3 (y 1 - y 2) ∣

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