Question

The area of the triangle formed by the points P(0,1), Q(0,5) and R(3,4) is
A. 16 sq. units
B. 8 sq. units
C. 4 sq. units
D. 6 sq. Units

Answer 1

Given : Points of the triangle P(0,1), Q(0,5) and R(3,4)

Let P (x1, y1), Q(x2, y2), R (x3, y3) are the vertices of a triangle.

Area of triangle = |1/2 (x1(y2 − y3) + x2 (y3 − y1 )+ x3 (y1 − y2 ))|

Area of ∆ = ½ [(0(5 - 4)+ 0(4 - 1) + 3(1 - 5)]

Area of ∆ = ½ [(0(1)+ 0(3) + 3(- 4)]

Area of ∆ = ½ [(0 + 0 + - 12)]

Area of ∆ = ½  × |- 12|

Area of ∆ = 6 sq. units

Hence the Area of ∆ is 6 sq. units.

Option (D) 6 sq. units is correct.

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Answer 2

Formula for finding the area:

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

Here,

x1 = 0

x2 = 0

x3 = 3

y1 = 1

y2 = 5

y3 = 4

Area = 1/2(0 (5-4) + 0 (4-1) + 3 (1-5))

Area = 1/2( 0 + 0 - 12)

Area = 1/2(-12)

Area = |-6| = 6

Thus, answer is (D) 6 sq units