Question

Area of the triangle formed by points (0,2) (2,0) and (0,0) equals

(A)2 sq. units (B)4 sq. units (C)8 sq. units (D)none of these​

Answer 1

GIVEN:

Coordinates of triangle are (0,2),(2,0) and (0,0).

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TO FIND:

Area of triangle formed

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SOLUTION:

Let us name the coordinates of triangle.

⇒ A(0,2)

⇒ B(2,0)

⇒ C(0,0)

⇒ X1=0

⇒ X2=2

⇒ X3=0

⇒ Y1=2

⇒ Y2=0

⇒ Y3=0

Now we have formula of area of triangle.

✬Ar. triangle=½[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

⇒½[0(0-0)+2(0-2)+0(2+1)]

⇒½[0+2(-2)+0]

⇒½[-4]

⇒ -2 sq units.

As area of triangle can't be negative so will take it positive.

Hence the area of triangle is 2 sq. units. ‎ ‎ ‎ ‎ ‎

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}$

✠ Area of the triangle formed by points (0,2) (2,0) and (0,0) equals -

(Some options are given below) -

(A)2 sq. units

(B)4 sq. units

(C)8 sq. units

(D)None of these

${\large{\bold{\rm{\underline{Solution}}}}}$

✠ Area of the triangle formed by points (0,2) (2,0) and (0,0) equals - ${\sf{\red{2 \: sq. \: unit}}}$ or ${\sf{\red{Option \: (A)}}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

According to the question here, (assumptions) with (cordinate)

$\; \; \; \; \; \;{\bullet}$ A(0,2)

$\; \; \; \; \; \;{\bullet}$ B(2,0)

$\; \; \; \; \; \;{\bullet}$ C(0,0)

Therefore, cordinate be

$\; \; \; \; \; \;{\bullet}$ x₁ = 0 ; y₁ = 2

$\; \; \; \; \; \;{\bullet}$ x₂ = 2 ; y₂ = 0

$\; \; \; \; \; \;{\bullet}$ x₃ = 0 ; y₃ = 0

Now according to the area of triangle ∆ formula, let's do it !..

➨ ½[x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

Let's put the values !..

➨ ½[0(0-2) + 2(0-2) + 0(2-0)

➨ ½[0 + (-4) + 0]

➨ ½(-4)

➨ ½ × -4

➨ -2 sq. units

Note - We can't take it in negative form henceforth, Area of the triangle formed by points (0,2) (2,0) and (0,0) equals 2 sq. units