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MAT Exam 2025 Paper

Question : 71 of 150

Marks: +1, -0

(5,3),(-5,-2)

(3,-

Solution:

Concept:

To find the area of a triangle from vertices, use the determinant formula, then divide twice the area by the base length to get the altitude.

Explanation:

Let

P(5,3)

Q(-5,-2)

, and

R(3,-8)

Area is given by

A=\frac{1}{2}\left|5(-2-(-8))+(-5)(-8-3)+3(3-(-2))\right|

Simplify each term:

A=\frac{1}{2}|5(6)+(-5)(-11)+3(5)|

A=\frac{1}{2}|30+55+15|=\frac{1}{2}(100)=50

So, Area

=50

square units.

Take

QR

as the base:

QR=\sqrt{(3-(-5))^2+(-8-(-2))^2}

QR=\sqrt{8^2+(-6)^2}=\sqrt{64+36}=10

Now, Area

=\frac{1}{2}\times \text{base} \times \text{altitude}

50=\frac{1}{2}\times 10 \times h=5h

h=10

Thus, altitude

=10

units.

Answer:

Area

=50\ \mathrm{cm}^2

and Altitude

=10\ \mathrm{cm}

, i.e., Option C.

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