Coordinate Geometry - Distance & Section Formula for Exams

Coordinate Geometry - Distance and Section Formula - Proof-based Questions - Applications

Q. Find the coordinates of the point that divides the line segment joining (1, 2) and (4, 6) in the ratio 1:2.

Solution

Using the section formula: P = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Correct Answer: B — (3, 4)

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

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, 1), B(4, 5), and C(7, 2), what is the perimeter of the triangle?

Solution

Perimeter = AB + BC + CA = √((4-1)² + (5-1)²) + √((7-4)² + (2-5)²) + √((1-7)² + (1-2)²) = 3 + √(9 + 9) + √(36 + 1) = 3 + 4.24 + 6.08 = 13.32.

Correct Answer: B — 14

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