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GUJCET 2025 Math Paper

Question : 1 of 40

Marks: +1, -0

(2, 7)

(1, 1)

(10, 8)

Solution:

Concept:

The triangle formed by the midpoints of the sides has area equal to one-fourth of the original triangle.

Explanation:

Let the given midpoints be

A(2,7)

B(1,1)

, and

C(10,8)

Find the area of triangle

ABC

using the coordinate formula.

\text{Area}_{ABC}=\frac12\left|2(1-8)+1(8-7)+10(7-1)\right|

Simplify the bracket:

2(-7)+1(1)+10(6)=-14+1+60=47

So,

\text{Area}_{ABC}=\frac12(47)=\frac{47}{2}

The original triangle area is

4

times this area.

\text{Area}_{\text{original}}=4\times \frac{47}{2}=94

Answer:

The area of the triangle is

94

(Option C).

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