{"id":1797,"date":"2024-05-28T13:47:54","date_gmt":"2024-05-28T04:47:54","guid":{"rendered":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1797"},"modified":"2024-06-17T12:50:03","modified_gmt":"2024-06-17T03:50:03","slug":"top-math2-2q2h-2","status":"publish","type":"post","link":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1797","title":{"rendered":"\u6570\u5b66II_2Q2H_2"},"content":{"rendered":"\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nBack<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u518d\u751f\u30ea\u30b9\u30c8<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
\u30c6\u30ad\u30b9\u30c8<\/span><\/td>\n\u6f14\u7fd2<\/span><\/td>\n\u6f14\u7fd2\u89e3\u7b54<\/span><\/td>\n\u8ab2\u984c<\/span><\/td>\n\u89e3\u8aac<\/span><\/td>\n<\/tr>\n
2Q2H_4<\/span><\/a><\/td>\n2Q2H_E4<\/span><\/a><\/td>\n2Q2H_ES4<\/span><\/a><\/td>\n2Q2H_K4<\/span><\/a><\/td>\n2Q2H_V4<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n2Q2H_pf4<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span> $|AB^\u2192|=?$\u3001AB\u3092$t:1-t$\u306b\u5206\u3051\u308b\u70b9$P=?$\u3001\u4e2d\u70b9$M=?$\u3001\u4e09\u89d2\u5f62$ABC$\u306e\u91cd\u5fc3$G=?$ <\/div>
${\\mathrm{A}}(a_1,a_2)$\u3001${\\mathrm{B}}(b_1,b_2)$\u3001${\\mathrm{C}}(c_1,c_2)$\u306e\u3068\u304d
\n\u70b9${\\mathrm{A}}$\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\uff1a$\\vec{a}=\\overrightarrow{\\mathrm{OA}}=\\begin{pmatrix}a_1 \\\\ a_2 \\end{pmatrix}$$\\quad |\\vec{a}|=|\\overrightarrow{\\mathrm{OA}}|=\\sqrt{a_1^2+a_2^2}$<\/span>
\n\u70b9${\\mathrm{B}}$\u3001${\\mathrm{C}}$\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3082\u540c\u69d8\u306b\u8868\u8a18\u3059\u308b
\n${\\mathrm{AB}}=|\\overrightarrow{\\mathrm{AB}}|=|-\\vec{a}+\\vec{b}|=\\left | \\begin{pmatrix}b_1-a_1 \\\\ b_2-a_2 \\end{pmatrix} \\right |=\\sqrt{(b_1-a_1)^2+(b_2-a_2)^2}$<\/span>
\n${\\mathrm{AB}}$ \u3092 $t:1-t$ \u306b\u5206\u3051\u308b\u70b9\u3092 ${\\mathrm{P}}$ \u4e2d\u70b9\u3092 ${\\mathrm{M}}$ \u3068\u3059\u308b\u3068
\n$\\quad \\overrightarrow{\\mathrm{OP}}=(1-t)\\vec{a}+t\\vec{b} \\quad \\overrightarrow{\\mathrm{OM}}=\\dfrac{1}{2}\\left(\\vec{a}+\\vec{b} \\right)$<\/span>
\n$\\triangle {\\mathrm{ABC}}$ \u306e\u91cd\u5fc3\u3092 ${\\mathrm{G}}$ \u3068\u3059\u308b\u3068 $\\quad \\overrightarrow{\\mathrm{OG}}=\\dfrac{1}{3}\\left(\\vec{a}+\\vec{b}+\\vec{c} \\right)$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. $\\triangle {\\mathrm{ABC}}$\u3092\u4e0e\u3048\u3066\u3001
\n$\\quad$$ {\\mathrm{AB}}=\\lvert \\overrightarrow{\\mathrm{AB}} \\rvert$\u3001$ {\\mathrm{BC}}=\\lvert \\overrightarrow{\\mathrm{BC}} \\rvert$\u3001$ {\\mathrm{CA}}=\\lvert \\overrightarrow{\\mathrm{CA}} \\rvert$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n2. \u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u8868\u793a\u3092\u5229\u7528\u3057\u3066\u3001
\n$\\quad$\u5185\u5206\u70b9\u30fb\u5916\u5206\u70b9\u30fb\u4e2d\u70b9<\/span> \u304a\u3088\u3073 \u4e09\u89d2\u5f62\u306e\u91cd\u5fc3<\/span> \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n
2Q2H_5<\/span><\/a><\/td>\n2Q2H_E5<\/span><\/a><\/td>\n2Q2H_ES5<\/span><\/a><\/td>\n2Q2H_K5<\/span><\/a><\/td>\n2Q2H_V5<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span>\u5782\u76f4\u6761\u4ef6 $a^\u2192\u22a5b^\u2192=?$\u3001\u5e73\u884c\u6761\u4ef6 $a^\u2192\/\/b^\u2192=?$<\/div>
$\\vec{a}=\\begin{pmatrix}a_1 \\\\ a_2 \\end{pmatrix}$\u3001$\\vec{b}=\\begin{pmatrix}b_1 \\\\ b_2 \\end{pmatrix}$ \u306e\u3068\u304d $\\quad \\vec{a}\\perp \\vec{b} \\Leftrightarrow \\vec{a}\\cdot\\vec{b}=a_1a_2+b_1b_2=0$<\/span>
\n$\\vec{a}\u3000\/\\!\/\u3000\\vec{b}\u3000\\Leftrightarrow \\vec{a}=t\\vec{b}$<\/span> $ \\Leftrightarrow \\begin{cases} a_1=tb_1 \\\\ a_2=tb_2 \\end{cases}$ $ \\Leftrightarrow \\begin{cases} \\dfrac{a_1}{b_1}=\\dfrac{a_2}{b_2}(=t) \\; (b_1b_2\\neq1) \\\\ a_1=0 \\; (b_1=0) \\\\ a_2=0 \\; (b_2=0) \\end{cases}$<\/span><\/div><\/div>\n
<\/span>Targets<\/div>
1. \u56db\u89d2\u5f62 $\\square {\\mathrm{ABCD}}$ \u304c\u5e73\u884c\u56db\u8fba\u5f62\u3068\u306a\u308b<\/span>\u6761\u4ef6
\n2. \uff13\u70b9 ${\\mathrm{A}}$\u3001 ${\\mathrm{B}}$\u3001${\\mathrm{C}}$ \u304c\u4e00\u76f4\u7dda\u4e0a\u306b\u4e26\u3076<\/span>\u3000\u6761\u4ef6
\n3. \u30d9\u30af\u30c8\u30eb $\\vec{a}$\u3001$\\vec{b}$ \u304c\u5782\u76f4\u3068\u306a\u308b<\/span>\u6761\u4ef6
\n\u4ee5\u4e0a\u3092\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u3042\u3089\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n
2Q2H_6<\/span><\/a><\/td>\n2Q2H_E6<\/span><\/a><\/td>\n2Q2H_ES6<\/span><\/a><\/td>\n2Q2H_K6<\/span><\/a><\/td>\n2Q2H_V6<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n2Q2H_pf6<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span>\u5b9a\u70b9\u3092\u901a\u308a\u3001\u30d9\u30af\u30c8\u30eb$v^\u2192$\u306b\u5e73\u884c\u306a\u76f4\u7dda $=?$\u3001\u30d9\u30af\u30c8\u30eb $n^\u2192$\u3000\u306b\u5782\u76f4\u306a\u76f4\u7dda\u3000$=?$
\n$AB$ \u3092\u76f4\u5f84\u306e\u4e21\u7aef\u3068\u3059\u308b\u5186 $=?$<\/div>
\u70b9${\\mathrm{A}}(x_1, x_2)$ \u3092\u901a\u308a
\n\u30d9\u30af\u30c8\u30eb $\\vec{v}=\\begin{pmatrix}a \\\\ b \\end{pmatrix}$ \u306b\u5e73\u884c\u306a\u76f4\u7dda\uff1a$\\dfrac{x-x_1}{a}=\\dfrac{y-y_1}{b}$<\/span>
\n\u30d9\u30af\u30c8\u30eb $\\vec{n}=\\begin{pmatrix}a \\\\ b \\end{pmatrix}$ \u306b\u5782\u76f4\u306a\u76f4\u7dda\uff1a$a(x-x_1)+b(y-y_1)$<\/span>
\n\uff12\u70b9 ${\\mathrm{A}}(x_1, y_1)$\u3001${\\mathrm{B}}(x_2, y_2)$ \u3092\u76f4\u5f84\u306e\u4e21\u7aef\u3068\u3059\u308b\u5186\uff1a
\n$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. \u70b9 ${\\mathrm{C}}$ \u3092\u901a\u308a\u30d9\u30af\u30c8\u30eb $\\overrightarrow{\\mathrm{AB}}$ \u306b\u5e73\u884c\u306a\u76f4\u7dda\u304a\u3088\u3073\u5782\u76f4\u306a\u76f4\u7dda<\/span>
\n$\\quad$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n2. \u7dda\u5206 ${\\mathrm{AB}}$ \u3092\u76f4\u5f84\u306e\u4e21\u7aef\u3068\u3059\u308b\u5186<\/span>\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n3. \u4e09\u89d2\u5f62 ${\\triangle \\mathrm{ABC}} $\u306e\u9802\u70b9\u3092\u901a\u308a\u3001 \u5bfe\u8fba\u306b\u5782\u76f4\u306a\u76f4\u7dda<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n$\\quad$\u307e\u305f\u3001\u4e09\u89d2\u5f62${\\triangle \\mathrm{ABC}}$\u306e\u5782\u5fc3<\/span>\u3082\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nBack<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 \u00a0 \u00a0 Back \u00a0 \u00a0 \u00a0 \u00a0 \u518d\u751f\u30ea\u30b9\u30c8 \u30c6\u30ad\u30b9\u30c8 \u6f14\u7fd2 \u6f14\u7fd2\u89e3\u7b54 \u8ab2\u984c \u89e3\u8aac 2Q2H_4 2Q2H_E4 2Q2H_ES4 2Q2H_K4 2Q2H_V4 \u00a0 \u00a0 \u00a0 \u00a0 2Q2H_pf4 2Q2H_5 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44,42,14,4,8,35],"tags":[],"class_list":["post-1797","post","type-post","status-publish","format-standard","hentry","category-math2-2q2h-2","category-si","category-top","category-math2","category-math2-2q","category-math2-2q2h-1"],"_links":{"self":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1797","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1797"}],"version-history":[{"count":83,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1797\/revisions"}],"predecessor-version":[{"id":2150,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1797\/revisions\/2150"}],"wp:attachment":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}