Question

COORDINATE GEOMETRY
CLASS 10
________________________

•Please answer all the given question in the picture.
________________________

THANKS...​ ​

Answer 1

Step-by-step explanation:

given three points are (t, t-2) , (t+2, t+2) and (t+3, t)

use formula of traingle form of co-ordinate geometry .

area of traingle =1/2 {x1 (y2-y3)+x2 (y3-y1)+x3(y1-y2)}

now,

ar of triangle=1/2 {t (t+2-t)+(t+2)(t-t+2)+(t+3 (t-2-t-2)}

=1/2 {2t +2t +4 -4t -12}

=1/2 {-8}

=-4

but here mention only magnitude of area of triangle so , area of traingle =4 sq unit

you see in area of triangle not depend upon t

Answer 2

We've been given three vertices of a Triangle, Let us name these three points A, B & C respectively.

A(t, t + 2)

B(t + 2, t + 2)

B(t + 3, t)

Let us name these three points A, B & C respectively. Now let's find the area of the triangle, and see if it's independent of t.

• x₁ = t
• x₂ = t + 2
• x₃ = t + 3
• y₁ = t + 2
• y₂ = t + 2
• y₃ = t

We know that area of a triangle can be written as:

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

⇒ ar(Δ) = ¹/₂ [t(t + 2 - t) + (t + 2)(t - (t + 2)) + (t + 3)(t + 2 - (t + 2))]

⇒ ar(Δ) = ¹/₂ [t(2) + (t + 2)(t - t - 2) + (t + 3)(t + 2 - t - 2))]

⇒ ar(Δ) = ¹/₂ [2t + (t + 2)(- 2) + (t + 3)(0))]

⇒ ar(Δ) = ¹/₂ [2t - 2t - 4]

⇒ ar(Δ) = ¹/₂ [- 4]

⇒ ar(Δ) = 2 sq.units.

(Area cannot be -ve, therefore we take it to be +ve)

The variable "t" isn't a part of the answer, hence the area of this triangle is independent of t.