Coordinate Geometry - Distance & Section Formula for Exams

Coordinate Geometry - Distance and Section Formula - Case Studies

Q. If a point P divides the segment joining A(2, 3) and B(8, 7) in the ratio 3:1, what are the coordinates of P?

Solution

Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (6, 5).

Correct Answer: B — (6, 5)

Q. If point A is at (2, 3) and point B is at (8, 7), what is the midpoint M of segment AB?

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Q. If point C is at (0, 0) and point D is at (6, 8), what is the length of segment CD?

Solution

Using the distance formula: d = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10.

Correct Answer: B — 10

Q. What is the ratio in which the point (3, 5) divides the line segment joining (1, 2) and (5, 8)?

Solution

Using the section formula, we find the ratio is 2:1.

Correct Answer: B — 2:1

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