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Find the area of the triangle whose vertices are (4,3) (1,4) and (2,3)

written 5.6 years ago by teamques10 ★ 69k

modified 3.0 years ago by pedsangini276 • 4.8k

engineering mathematics

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1 Answer

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written 5.6 years ago by teamques10 ★ 69k

•   modified 5.6 years ago

Solution:

$Let \left(x_{1}, y_{1}\right)=(4,3),\left(x_{2}, y_{2}\right)=(1,4) and \left(x_{3}, y_{3}\right)=(2,3)$

$$\begin{aligned} A=\frac{1}{2}\left|\begin{array}{ccc}{x_{1}} & {y_{1}} & {1} \ {x_{2}} & {y_{2}} & {1} \ {x_{3}} & {y_{3}} & {1}\end{array}\right| \ =& \frac{1}{2}\left|\begin{array}{ccc}{4} & {3} & {1} \ {1} & {4} & {1} \ {2} & {3} & {1}\end{array}\right| \ =& \frac{1}{2}[4(4-3)-3(1-2)+1(3-8)] \=& 1 \end{aligned}$$

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