Find the area of $Δ$ PQR whose vertices are P (2,1), Q (3, 4) and R (5, 2).

Open in App

Solution

Given $Δ P Q R P (2, 1), Q (3, 4), R (5, 2)$

Area of $Δ$ with vertices $(x_{1}, y_{2}) (x_{2}, y_{2}), (x_{3}, y_{3})$

$Δ = \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣$

$∴ Δ = \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 3 & 4 & 1 5 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣$

$= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 1 & 3 & 0 3 & 1 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$R_{2} \to R_{2} - R_{1}$

$R_{3} \to R_{3} - R_{1}$

$= \frac{1}{2} | 1 [9 - 1] |$

$= \frac{8}{2} = 4$ sq. units

Suggest Corrections

Similar questions

△ P Q R

P (2, 1), Q (3, 4)

R (5, 2)

P Q R S - ------ -

P (- 5, - 3), Q (- 4, - 6), R (2, - 1)

S (1, 2)

P Q R

P (2, 5), Q (4, 7)

R (6, 2)

The area of the quadrilateral PQRS whose vertices are P (-5, 7), Q (-4, -5), R (-1, -6) and S (4, 5) is

Join BYJU'S Learning Program