Matika - 9. ročník - 2024 / Jan Samec

Jan Samec

Workspace

Public

Edited

Dec 16

Fork of Matika - 9. ročník - 1. řádný termín

•

1 fork

smartDrawing(300, (rac, shared) => {

const A = rac.Point(74, 208);

const E = rac.Point(232, 153);

const P = rac.Point(121, 41);

let rayAE = A.rayToPoint(E);

let p = P.rayToPoint(E);

let SegmentAE = A.distanceToPoint(E);

const calibration = rac

.Composite([

markPoint(rac, A, "A", rac.Text.Format.tc),

markPoint(rac, E, "E", rac.Text.Format.bc),

rayAE,

p.text("p").upright()

])

.draw();

let k = A.arc(SegmentAE);

let C = k.intersectionChordWithRay(p).startPoint();

let r = rayAE.perpendicular(false).translateToDistance(-50);

let q = C.rayToProjectionInRay(rayAE);

let s = C.rayToProjectionInRay(r);

let B = rayAE.pointAtIntersection(q);

let D = s.pointAtIntersection(r);

const kresleni = rac

.Composite([

markPoint(rac, C, "C", rac.Text.Format.bc),

r.text("r").upright(),

q.text("q").upright(),

markPoint(rac, B, "B", rac.Text.Format.tr),

markPoint(rac, D, "D", rac.Text.Format.bl)

])

.draw(shared.secondary);

polygon(rac, [A, B, C, D]).draw(shared.primary);

})

smartDrawing(300, (rac, shared) => {

const L = rac.Point(205,227)

const S = rac.Point(172,130)

const K = rac.Point(105,180)

const k = rac.Point(113,94)

let DistancSk = S.distanceToPoint(k)

let arck = S.arc(DistancSk)

let segmentKL = K.segmentToPoint(L)

let DistancKL = K.distanceToPoint(L)

let m = K.arc(DistancKL)

let M1 = m.intersectionArc(arck).endPoint();

let M2 = m.intersectionArc(arck).startPoint();

const calibration = rac

.Composite([

markPoint(rac, L, "L", rac.Text.Format.cl),

markPoint(rac, S, "S", rac.Text.Format.bc),

markPoint(rac, K, "K", rac.Text.Format.cr),

arck,

k.text("k",rac.Text.Format.br),

segmentKL,

])

.draw();

const reseni = rac

.Composite([

segmentKL,

markPoint(rac, M1, "M1", rac.Text.Format.tl),

markPoint(rac, M2, "M2", rac.Text.Format.bc),

])

.draw(shared.secondary);

polygon(rac, [K,L,M1,]).draw(shared.primary);

polygon(rac, [K,L,M2,]).draw(shared.primary);

})

mdPlus`${questionsD[8].content()}`

smartDrawing(300, (rac, shared) => {

const A = rac.Point(89, 132);

const S = rac.Point(140, 118);

const p = rac.Point(48, 90);

const p2 = rac.Point(260, 72);

let rayp = p.rayToPoint(p2);

const calibration = rac

.Composite([

markPoint(rac, S, "S", rac.Text.Format.bc),

markPoint(rac, A, "A", rac.Text.Format.cr),

p.text("p", rac.Text.Format.rb),

rayp

])

.draw();

let rayAS = A.rayToPoint(S);

let DistancAS = A.distanceToPoint(S);

let arck = S.arc(DistancAS);

let C = arck.intersectionChordWithRay(rayAS).endPoint();

let D1 = arck.intersectionChordWithRay(rayp).startPoint();

let D2 = arck.intersectionChordWithRay(rayp).endPoint();

let rayD1S = D1.rayToPoint(S);

let B2 = arck.intersectionChordWithRay(rayD1S).endPoint();

let rayD2S = D2.rayToPoint(S);

let B1 = arck.intersectionChordWithRay(rayD2S).endPoint();

const reseni = rac

.Composite([

rayAS,

arck,

markPoint(rac, C, "C", rac.Text.Format.cl),

markPoint(rac, D1, "D1", rac.Text.Format.br),

markPoint(rac, D2, "D2", rac.Text.Format.bl),

rayD1S,

markPoint(rac, B2, "B2", rac.Text.Format.tc),

rayD2S,

markPoint(rac, B1, "B1", rac.Text.Format.tc)

])

.draw(shared.secondary);

polygon(rac, [A, B2, C, D2]).draw(shared.primary);

polygon(rac, [A, B1, C, D1]).draw(shared.primary);

})

mdPlus`${questionsD[9].content()}`

smartDrawing(300, (rac, shared) => {

const C = rac.Point(75, 78);

const S = rac.Point(157, 91);

const p = rac.Point(273, 114);

const P2 = rac.Point(103, 206);

let rayp = p.rayToPoint(P2);

const calibration = rac

.Composite([

markPoint(rac, S, "S", rac.Text.Format.bc),

markPoint(rac, C, "C", rac.Text.Format.bc),

p.text("p", rac.Text.Format.tc),

rayp

])

.draw();

let rayCS = C.rayToPoint(S);

let DistancCS = C.distanceToPoint(S);

let arck = S.arc(DistancCS);

let B = arck.intersectionChordWithRay(rayCS).endPoint();

let p2 = rayp.translatePerpendicular(rayp.distanceToProjectedPoint(B));

let r = C.rayToProjectionInRay(p2);

let m = rayCS.perpendicular(true);

let A2 = p2.pointAtIntersection(m);

let A1 = r.pointAtIntersection(p2);

const reseni = rac

.Composite([

rayCS,

arck,

markPoint(rac, B, "B", rac.Text.Format.br),

p2,

markPoint(rac, A2, "A2", rac.Text.Format.tl),

markPoint(rac, A1, "A1", rac.Text.Format.tl)

])

.draw(shared.secondary);

polygon(rac, [A1, B, C]).draw(shared.primary);

polygon(rac, [A1, C, A2]).draw(shared.primary);

})

viewof point = imagePointPicker({imageUrl:'https://www.eforms.cz/math/4/M9D-2024/image-3.png', height: 300})

import {toc} from "@harrystevens/toc@129"

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