Question

Find the area of triangle PQR formed by the points P(-5,7), Q(-4,-5) and R(4,5).​

Answer 1

Given:

✰ Point P( -5, 7 )

✰ Point Q( -4, -5 )

✰ Point R ( 4, 5 )

To find:

✠ The area of triangle PQR

Solution:

Consider,

In point P( -5, 7 )

✫ -5 = x₁

✫ 7 = y₁

In point Q( -4, -5 )

✫ -4 = x₂

✫ -5 = y₂

In point R ( 4, 5 )

✫ 4 = x₃

✫ 5 = y₃

Now,

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

• Area of ∆PQR = 1/2 [ -5( -5 - 5 ) -4( 5 - 7 ) +4( 7 + 5 )]

• Area of ∆PQR = 1/2 [ ( 25 + 25 ) + ( - 20 + 28 ) + ( 28 + 20 ) ]

• Area of ∆PQR = 1/2 [ 50 + 8 + 48 ]

• Area of ∆PQR = 1/2 [ 58 + 48 ]

• Area of ∆PQR = 1/2 [ 58 + 48 ]

• Area of ∆PQR = 1/2 [ 106 ]

• Area of ∆PQR = 1/2 × 106

• Area of ∆PQR = 53 sq.unit

∴ The ∆ of triangle PQR = 53 sq.unit

Signs:

• + + = +

• - - = +

• - + = -

• + - = -

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