Question

find the area of the ∆ PQR whose vertices are P (5,2) ,Q (-3,7) and R (2,-4) ​

Answer 1

Solution!!

The concept of co-ordinate geometry has to be used here. The vertices of a triangle are given in the question. We are asked to find the area of the triangle.

P(5 , 2)

Q(-3 , 7)

R(2 , -4)

Now, let's use a suitable formula to find the area of the triangle.

Area = 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Here,

x₁ = 5

x₂ = -3

x₃ = 2

y₁ = 2

y₂ = 7

y₃ = -4

Area = 1/2[5(7 - (-4)) + (-3)(-4 - 2) + 2(2 - 7)]

Area = 1/2[5(7 + 4) + (-3)(-6) + 2(-5)]

Area = 1/2[5(11) + 18 - 10]

Area = 1/2[55 + 18 - 10]

Area = 1/2[63]

Area = 31.5 sq units