Markaziy nuqta formulasi

Koordinata tekisligida yotgan ikkita nuqta $(\greenD{x_1}, \goldD{y_1})$left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis va $(\greenD{x_2}, \goldD{y_2})$left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis $\blueD{\text{oʻrtasidagi nuqta}}$start color #11accd, start text, o, ʻ, r, t, a, s, i, d, a, g, i, space, n, u, q, t, a, end text, end color #11accd quyidagi formula orqali hisoblanadi:

Ushbu maqolada mazkur formulani oʻzimiz keltirib chiqaramiz!

Keling, ishni oldin $(\greenD{x_1}, \goldD{y_1})$left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis va $(\greenD{x_2}, \goldD{y_2})$left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis nuqtalarni yasashdan boshlaymiz.

$\blueD{\text{Markaziy nuqta}}$start color #11accd, start text, M, a, r, k, a, z, i, y, space, n, u, q, t, a, end text, end color #11accd bu har bir nuqtagacha boʻlgan yarim masofadir:

$x$x-koordinatasidagi $\blueD{\text{nuqtalar oʻrtasini }}$start color #11accd, start text, n, u, q, t, a, l, a, r, space, o, ʻ, r, t, a, s, i, n, i, space, end text, end color #11accd topish ifodasi $\greenD{\dfrac{x_1+x_2}{2}}$start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54:

Shuningdek, $y$y-koordinatasidagi $\blueD{\text{nuqtalar oʻrtasini}}$start color #11accd, start text, n, u, q, t, a, l, a, r, space, o, ʻ, r, t, a, s, i, n, i, end text, end color #11accd topish ifodasi $\goldD{\goldD{\dfrac{y_1+y_2}{2}}}$start color #e07d10, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, end color #e07d10:

Ana boʻldi! Quyidagi formulani biz $\blueD{\text{nuqtalar oʻrtasini}}$start color #11accd, start text, n, u, q, t, a, l, a, r, space, o, ʻ, r, t, a, s, i, n, i, end text, end color #11accd topish uchun keltirib chiqardik:

Qizigʻi shundaki, koʻpchilik bu formulaning aynan oʻzini eslab qolishmaydi. Uning oʻrniga nuqtalar oʻrtasini topish uchun $x$x va $y$y-koordinatalarining oʻrtachasi olinadi deb hisoblashadi.