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With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal to
  • a)
    3/2
  • b)
    3/4
  • c)
    4/5
  • d)
    5/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
With reference to the conventional Cartesian (x, y) coordinate system,...
Given:
The coordinates of the vertices of the triangle are:
(x1, y1) = (1, 0)
(x2, y2) = (2, 2)
(x3, y3) = (4, 3)

To Find:
The area of the triangle.

Approach:
To find the area of a triangle in a Cartesian coordinate system, we can use the Shoelace formula. The Shoelace formula states that the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by:

Area = |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))/2|

Here, |x| represents the absolute value of x.

Calculation:
We can substitute the given coordinates into the Shoelace formula to find the area of the triangle.

Area = |(1(2 - 3) + 2(3 - 0) + 4(0 - 2))/2|
= |(-1 + 6 - 8)/2|
= |-3/2|
= 3/2

Therefore, the area of the triangle is 3/2.

Answer:
The correct option is A) 3/2.
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With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal toa)3/2b)3/4c)4/5d)5/2Correct answer is option 'A'. Can you explain this answer?
Question Description
With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal toa)3/2b)3/4c)4/5d)5/2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal toa)3/2b)3/4c)4/5d)5/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal toa)3/2b)3/4c)4/5d)5/2Correct answer is option 'A'. Can you explain this answer?.
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