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GMAT - Problem Solving - Coordinate geometry

In the rectangular coordinate system above, the area of triangular region PQR is

In the rectangular coordinate system above, the area of triangular region PQR is

Area of a triangle is given by: 

Mod (\frac { 1 }{ 2 } ({ x }_{ 2 }{ y }_{ 3 }-{ y }_{ 2 }x_{ 3 }+{ x }_{ 3 }{ y }_{ 1 }-{ y }_{ 3 }{ x }_{ 1 }+{ x }_{ 1 }{ y }_{ 2 }-{ y }_{ 1 }{ x }_{ 2 }))

= mod( 1/2(0*4 - 3*7 + 7*0 - 4*4 - 4*3 - 0*0)

= mod(1/2(-21 - 16 - 12)

=mod(1/2(-25)

= mod(-12.5)

= 12.5 units2

Area of a triangle is given by: 

Mod (\frac { 1 }{ 2 } ({ x }_{ 2 }{ y }_{ 3 }-{ y }_{ 2 }x_{ 3 }+{ x }_{ 3 }{ y }_{ 1 }-{ y }_{ 3 }{ x }_{ 1 }+{ x }_{ 1 }{ y }_{ 2 }-{ y }_{ 1 }{ x }_{ 2 }))

= mod( 1/2(0*4 - 3*7 + 7*0 - 4*4 - 4*3 - 0*0)

= mod(1/2(-21 - 16 - 12)

=mod(1/2(-25)

= mod(-12.5)

= 12.5 units2