Given two coordinates (x1, y1) and (x2, y2), and m and n, find the co-ordinates that divides that divides the line joining (x1, y1) and (x2, y2) in the ratio m : n
Input : x1 = 1, y1 = 0, x2 = 2 y2 = 5, m = 1, n = 1 Output : (1.5, 2.5) Explanation: co-ordinates (1.5, 2.5) divides the line in ratio 1 : 1 Input : x1 = 2, y1 = 4, x2 = 4, y2 = 6, m = 2, n = 3 Output : (2.8, 4.8) Explanation: (2.8, 4.8) divides the line in the ratio 2:3
The section formula tells us the coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m : n
How does this work?
From our diagram, we can see, PS = x – x1 and RT = x2 – x We are given, PR/QR = m/n Using similarity, we can write RS/QT = PS/RT = PR/QR Therefore, we can write PS/RR = m/n (x - x1) / (x2 - x) = m/n From above, we get x = (mx2 + nx1) / (m + n) Similarly, we can solve for y.
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