Question

COORDINATE GEOMETRY
CLASS 10
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•Please answer the given question in the picture.
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THANKS...​ ​

Answer 1

Corrected question: Find the area of the parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3, 5) and C(2, 6).

We know that the diagonals in a parallelogram divide it into two equal triangles, and both triangles have the same area.

Therefore, we'll find the area of the triangle formed by the points A(2, 4), B(2 + √3, 5) and C(2, 6) then multiply it by 2 to get the answer.

Hence:

A(2, 4) → (x₁, y₁)

B(2 + √3, 5) → (x₂, y₂)

C(2, 6) → (x₃, y₃)

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

ar(ΔABC) = ¹/₂ [2(5 - 6) + (2+ √3)(6 - 4) + 2(4 - 5)]

ar(ΔABC) = ¹/₂ [2(-1) + (2+ √3)(2) + 2(-1)]

ar(ΔABC) = ¹/₂ [-2 + 4 + 2√3 - 2]

ar(ΔABC) = ¹/₂ [2 + 2√3 - 2]

ar(ΔABC) = ¹/₂ [2√3]

ar(ΔABC) = √3 sq.units.

ar(Parallelogram) = ar(ABC) × 2

ar(Parallelogram) = √3 × 2

ar(Parallelogram) = 2√3 sq.units.

Answer 2

Answer:

Corrected question: Find the area of the parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3, 5) and C(2, 6).

We know that the diagonals in a parallelogram divide it into two equal triangles, and both triangles have the same area.

Therefore, we'll find the area of the triangle formed by the points A(2, 4), B(2 + √3, 5) and C(2, 6) then multiply it by 2 to get the answer.

Hence:

A(2, 4) → (x₁, y₁)

B(2 + √3, 5) → (x₂, y₂)

C(2, 6) → (x₃, y₃)

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

ar(ΔABC) = ¹/₂ [2(5 - 6) + (2+ √3)(6 - 4) + 2(4 - 5)]

ar(ΔABC) = ¹/₂ [2(-1) + (2+ √3)(2) + 2(-1)]

ar(ΔABC) = ¹/₂ [-2 + 4 + 2√3 - 2]

ar(ΔABC) = ¹/₂ [2 + 2√3 - 2]

ar(ΔABC) = ¹/₂ [2√3]

ar(ΔABC) = √3 sq.units.

ar(Parallelogram) = ar(ABC) × 2

ar(Parallelogram) = √3 × 2

ar(Parallelogram) = 2√3 sq.units.