[wanted]useful maths formula

YTC

2015-03-06 7:16 pm

My teacher told me a powerful formula that is not in the syllabus of HKDSE:
the distance betwwen a line ax + by + c = 0 and a point (x0,y0)
= |x0+by0+c| / √(a^2 + b^2)

I found that it is faster and the calculation is simple than using some basic
formula. So I want to ask for some useful,faster formula that do not in the HKDSE syllabus but the formula can easily let me know how to sub the numbers into the
formula. Thank you!!

回答 (1)

邊位都好

2015-03-09 12:28 am

✔ 最佳答案

To calculate the area of a n-sides polygon on the x-y plane.
Let P1(x1, y1), P2(x2, y2), P3(x3, y3), ... , Pn(xn, yn)and all points are in anti-clockwise direction. Then the area is(1/2)*[x1*y2 + x2*y3 + ... + (xn-1)*yn + xn*y1 - y1*x2 - y2*x3 - ... - (yn-1)*xn - yn*x1]

For example, a quadrilateral with P1(-1, -2), P2(2, -5), P3(6, 7), P4(-3, 4), it's area is :
(1/2)*[(-1)*(-5) + 2*7 + 6*4 + (-3)*(-2) - (-2)*2 - (-5)*6 - 7*(-3) - 4*(-1)]
= (1/2)*(5 + 14 + 24 + 6 + 4 + 30 + 21 + 4)
= 54 (sq. units)

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