Class 10 · Chapter 7 · Interactive Lab
Coordinate geometry turns distance, midpoints and shapes into arithmetic. Drag the pins on each blueprint below the way a surveyor plants stakes on a plot — the formulas update live underneath.
Town A and town B, joined by a right triangle of legs dx and dy. Drag pin A (cyan) and pin B (coral) — the dashed legs are the Pythagoras construction from the textbook, and the hypotenuse is the distance.
Formula: PQ = √[(x₂−x₁)² + (y₂−y₁)²]
● A and ● B are draggable
A special case of the distance formula where one point is the origin O(0,0). Drag the amber pin — watch OP update.
Formula: OP = √(x² + y²)
● P is draggable · O is fixed at the origin
Point P divides AB internally in the ratio m₁ : m₂. Drag A and B, then slide the ratio — P slides along the segment exactly like the relay-tower example in the chapter.
Formula: P = ( (m₁x₂+m₂x₁)/(m₁+m₂), (m₁y₂+m₂y₁)/(m₁+m₂) )
● A · ● B · ● P divides A→B
The midpoint is the section formula at ratio 1:1. The trisection points split AB into three equal parts using ratios 1:2 and 2:1. Toggle the mode and drag A, B.
Midpoint: ( (x₁+x₂)/2, (y₁+y₂)/2 )
● A · ● B · ● markers computed
Every point equidistant from A and B lies on the perpendicular bisector of AB. Drag A and B — the bisector line is drawn live, and the point where it crosses the y-axis is solved exactly as in Example 5.
Locus condition: AP² = BP²
● A · ● B · ┄ perpendicular bisector
Drag three or four pins and let the distance formula tell you what shape you've built — scalene, isosceles, equilateral, right triangle, collinear, square, rectangle, rhombus, parallelogram, or none of those.
● A ● B ● C ● D