Question

Find the area of triangle whose vertices are represented by coordinates A( 2, 5),B( 1 , 1 ) and C(2,3)​

Answer 1

Answer:

1 units²

Explanation:

In a triangle ABC , the coordinates of the vertices are :-

• A(2, 5)
• B(1, 1)
• C(2, 3)

Area of the triangle is given by,

$\rm = \dfrac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Where,

• $\rm x_1 = 2 \:\&\: y_1 = 5$
• $\rm x_2 = 1 \:\&\: y_2 = 1$
• $\rm x_3 = 2 \:\&\: y_3 = 3$

Substituting the values,

${ = \dfrac{1}{2} |2(1 - 3) + 1(3 - 5) + 2(5 - 1)| }$

$= \dfrac{1}{2} |2( - 2) + 1( - 2) + 2(4)|$

$= \dfrac{1}{2} | - 4 - 2 + 8|$

$= \dfrac{1}{2} | - 6 + 8|$

$= \dfrac{1}{2} |2|$

$\rm \: = 1 \: unit {s}^{2}$

Hence, the area of the triangle is 1 units²

_____________________

Formula used :

• $\rm = \dfrac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Answer 2

Answer:

ANSWER = 1 unit square ( 1 unit ²)

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