Coordinate Geometry - Distance & Section Formula for Exams

Coordinate Geometry - Distance and Section Formula - Proof-based Questions - Case Studies

Q. If a triangle has vertices at A(0, 0), B(4, 0), and C(0, 3), what is the area of the triangle?

Solution

Area = (1/2) * base * height = (1/2) * 4 * 3 = 6.

Correct Answer: A — 6

Q. If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7, 2), what is the perimeter of the triangle?

Solution

Perimeter = AB + BC + CA = √((4-1)² + (6-2)²) + √((7-4)² + (2-6)²) + √((1-7)² + (2-2)²) = 3 + 5 + 6 = 14.

Correct Answer: B — 14

Q. What is the distance from the point (1, -1) to the line 2x + 3y - 6 = 0?

Solution

Distance = |Ax1 + By1 + C| / √(A² + B²) = |2*1 + 3*(-1) - 6| / √(2² + 3²) = |-7| / √13 = 7/√13.

Correct Answer: A — 2

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