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Question: The area of the triangle with vertices at \(( - 4,\ 1),(1,\ 2),(4,\ - 3)\) is....

The area of the triangle with vertices at (−4, 1),(1, 2),(4, −3)( - 4,\ 1),(1,\ 2),(4,\ - 3) is.

A

14

B

16

C

15

D

None of these

Answer

14

Explanation

Solution

Area of triangle =12∣x1y11x2y21x3y31∣= \frac { 1 } { 2 } \left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\ x _ { 2 } & y _ { 2 } & 1 \\ x _ { 3 } & y _ { 3 } & 1 \end{array} \right|

=12∣−4111214−31∣= \frac { 1 } { 2 } \left| \begin{array} { c c c } - 4 & 1 & 1 \\ 1 & 2 & 1 \\ 4 & - 3 & 1 \end{array} \right|

= 12[−4(2+3)−1(1−4)+1(−3−8)\frac { 1 } { 2 } [ - 4 ( 2 + 3 ) - 1 ( 1 - 4 ) + 1 ( - 3 - 8 )

=12∣−28∣=14= \frac { 1 } { 2 } | - 28 | = 14 units.