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Chapter 4: Q49. (page 187)

Find the area of the triangle ABC.

A.10squareunitsB.12squareunitsC.14squareunitsD.16squareunitsE.Noneofthese

Short Answer

Expert verified

The area of the triangle is 14 square units.

Step by step solution

01

Step 1- Check the figure.

Consider the figure.

The vertices from the graph are as follows:

A(x1,y1)=(2,3)B(x2,y2)=(1,−3)C(x3,y3)=(−3,1)

02

Step 2- Step description.

The area of the triangle can be calculated by the following formula:

A=12x1y2-y3+x2y3-y1+x3y1-y2

03

Step 3- Step description.

Substitute the values in the formula and simplify as follows:

A=12[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]A=12[2(−3−1)+1(1−3)+(−3)(3+3)]A=12[2(−4)−2−3(6)]A=12[−8−2−18]A=12(−28)A=−14

As area cannot be negative then consider only the numerical value 14.

Therefore, the area of the triangle is 14 square units.

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