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Question Number 98728 by Tinku Tara last updated on 15/Jun/20

Currently working on enhancing this app to draw shapes. So posting a math problem realted to drawing.^� Ref. Frame1 X-Y Frame 2: Axis translated by (h,k) and rotated about point (u,v). Consider a point (x_1 ,y_1 ) on X−Y axis. 1. What will be the postion of the point on X−Y axis after it is translated and plotted in frame 2. 2. A point is moved by distance dx,dy in X−Y. How much distane will it moved in the new frame.

$$\mathrm{Currently}\:\mathrm{working}\:\mathrm{on}\:\mathrm{enhancing} \\ $$$$\mathrm{this}\:\mathrm{app}\:\mathrm{to}\:\mathrm{draw}\:\mathrm{shapes}. \\ $$$$\mathrm{So}\:\mathrm{posting}\:\mathrm{a}\:\:\mathrm{math}\:\mathrm{problem}\:\mathrm{realted} \\ $$$$\mathrm{to}\:\mathrm{drawing}\bar {.} \\ $$$$\mathrm{Ref}.\:\mathrm{Frame1}\:\mathrm{X}-\mathrm{Y} \\ $$$$\mathrm{Frame}\:\mathrm{2}: \\ $$$$\mathrm{Axis}\:\mathrm{translated}\:\mathrm{by}\:\left({h},{k}\right)\:\mathrm{and} \\ $$$$\mathrm{rotated}\:\mathrm{about}\:\mathrm{point}\:\left({u},{v}\right). \\ $$$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{point}\:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right)\:\mathrm{on}\:\mathrm{X}−\mathrm{Y}\:\mathrm{axis}. \\ $$$$\mathrm{1}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{postion}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{X}−\mathrm{Y}\:\mathrm{axis}\:\mathrm{after}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{translated}\:\mathrm{and}\:\mathrm{plotted}\:\mathrm{in}\:\mathrm{frame}\:\mathrm{2}. \\ $$$$\mathrm{2}.\:\mathrm{A}\:\mathrm{point}\:\mathrm{is}\:\mathrm{moved}\:\mathrm{by}\:\mathrm{distance} \\ $$$${dx},{dy}\:\mathrm{in}\:\mathrm{X}−\mathrm{Y}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{distane} \\ $$$$\mathrm{will}\:\mathrm{it}\:\mathrm{moved}\:\mathrm{in}\:\mathrm{the}\:\mathrm{new}\:\mathrm{frame}. \\ $$

Commented by Tinku Tara last updated on 15/Jun/20

A more difficult problem: What will the postion of 3D point (x,y,z) in in 2D plane when viewed by a point observer at (a,b,c).

$$\mathrm{A}\:\mathrm{more}\:\mathrm{difficult}\:\mathrm{problem}: \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{the}\:\mathrm{postion}\:\mathrm{of}\:\mathrm{3D}\:\mathrm{point} \\ $$$$\left({x},{y},{z}\right)\:\mathrm{in}\:\mathrm{in}\:\mathrm{2D}\:\mathrm{plane}\:\mathrm{when}\:\mathrm{viewed} \\ $$$$\mathrm{by}\:\mathrm{a}\:\mathrm{point}\:\mathrm{observer}\:\mathrm{at}\:\left({a},{b},{c}\right). \\ $$

Commented by Tinku Tara last updated on 15/Jun/20

From software implementation point of view libraries do this computation internally.

Commented by MWSuSon last updated on 15/Jun/20

That will be wonderful sir.��

Commented by niroj last updated on 15/Jun/20

it's better Tinku tara if you make 2D shape for geometric shape , diagrams ,pie charts , triangle in high resulation edited and data collection like statistics table, more set notation or curve tracing map etc. ..

Commented by Tinku Tara last updated on 15/Jun/20

The post was meant to be a geometry question.��

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