Question

The area of the $\triangle A B C$, coordinates of whose vertices are $A(2,0), B(4,5)$ and $C(6,3)$ is .........

Name: Problem 49, Chapter 3: Integral Calculus IIT JEE
Uploaded: 2021-07-24T16:25:16-08:00
Duration: 2 min 56 s
Channel: Vikash Ranjan
Description: The area of the A B C, coordinates of whose vertices are A(2,0), B(4,5) and C(6,3) is .........

   The area of the $\triangle A B C$, coordinates of whose vertices are $A(2,0), B(4,5)$ and $C(6,3)$ is .........

Integral Calculus IIT JEE

Amit M Agarwal 2018 Edition

Chapter 3, Problem 49

Instant Answer

Solved by Expert Vikash Ranjan

07/24/2021

Step 1

The coordinates of the vertices of the triangle are given as $A(2,0)$, $B(4,5)$ and $C(6,3)$. The equation of line AB is given by $y - 0 = \frac{5}{2}(x - 2)$, which simplifies to $y = \frac{5}{2}x - 5$. The equation of line BC is given by $y - 5 = Show more…

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The area of the $\triangle A B C$, coordinates of whose vertices are $A(2,0), B(4,5)$ and $C(6,3)$ is .........

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Key Concepts

Shoelace Formula

The shoelace formula is a method for calculating the area of a polygon, most commonly used for triangles. It involves taking the coordinates of the vertices, multiplying and summing them in a specific order, and then computing the absolute difference of these sums divided by 2.

Coordinate Geometry

Coordinate geometry (or analytic geometry) connects algebra and geometry by using a coordinate system to represent geometric figures. In problems like these, the coordinates of the vertices are used to perform algebraic calculations to find properties, such as the area of a triangle.

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